text:
Franz-Viktor Kuhlmann's
Abstracts of Talks
Talk at the model theory seminar, Oxford 2016
Extremal fields and tame fields
In the year 2003 Yuri Ershov gave a talk at a conference in Teheran on his notion of ``extremal valued fields''. He proved that algebraically complete discretely valued fields are extremal. However, the proof contained a mistake, and it turned out in 2009 through an observation by Sergej Starchenko that Ershov's original definition leads to all extremal fields being algebraically closed. In joint work with Salih Durhan (formerly Azgin) and Florian Pop, we chose a more appropriate definition and then characterized extremal valued fields in several important cases.
We call a valued field (K,v) extremal if for all natural numbers n and all polynomials f in K[X_1,...,X_n], the set of values {vf(a_1,...,a_n) | a_1,...,a_n in the valuation ring} has a maximum (which is allowed to be infinity, attained if f has a zero in the valuation ring). This is such a natural property of valued fields that it is in fact surprising that it has apparently not been studied much earlier. It is also an important property because Ershov's original statement is true under the revised definition, which implies that in particular all Laurent Series Fields over finite fields are extremal. As it is a deep open problem whether these fields have a decidable elementary theory and as we are therefore looking for complete recursive axiomatizations, it is important to know the elementary properties of them well. That these fields are extremal could be an important ingredient in the determination of their structure theory, which in turn is an essential tool in the proof of model theoretic properties.
The notion of "tame valued field" and their model theoretic properties play a crucial role in the characterization of extremal fields. A valued field K with separable-algebraic closure K^sep is tame if it is henselian and the ramification field of the extension K^sep|K coincides with the algebraic closure. Open problems in the classification of extremal fields have recently led to new insights about elementary equivalence of tame fields in the unequal characteristic case. This led to a follow-up paper. Major suggestions from the referee were worked out jointly with Sylvy Anscombe and led to stunning insights about the role of extremal fields as ``atoms'' from which all aleph_1-saturated valued fields are pieced together.
Talk at the conference Ordered Algebraic Structures and Related Topics, CIRM, Luminy (France), October 12-16, 2015
Symmetrically complete ordered fields
(joint work with Katarzyna Kuhlmann)
Which are the ordered fields in which every descending chain of nonempty closed intervals has a nonempty intersection? This is true for the reals, but are there other ordered fields that have this property? Or does it imply that the field is cut complete and hence isomorphic to the reals? The clue is that you can zoom in on a cut using a descending chain of nonempty closed intervals only if the cofinality of the left cut set is equal to the coinitiality of the right cut set; we call such cuts "symmetrical". Hence an ordered field has the above property if and only if it has no symmetrical cuts; we call such fields (and other ordered structures) "symmetrically complete". In [1] we have shown that such fields satisfy an interesting fixed point theorem; It is quite similar to Banach's fixed point theorem although the fields need not be archimedean ordered.
Saharon Shelah [3] showed in 2004 that every ordered field can be extended to a symmetrically complete field. In joint work [2] with Katarzyna and Saharon, we have given a direct construction of such fields using power series. We construct first symmetrically complete linear orderings, then symmetrically complete ordered Hahn groups having these as their index sets and archimedean components isomorphic to the reals. In fact, we also show that every symmetrically complete ordered abelian group must be of this form, hence in particular divisible. Similarly, the power series fields over the reals with symmetrically complete value groups (plus a minor additional condition) are symmetrically complete ordered fields. Conversely, every symmetrically complete ordered field is of this form, hence in particular real closed.
[1] Kuhlmann, F.-V. and Kuhlmann, K.: A common generalization of metric, ultrametric and topological fixed point theorems, Forum Math. 27 (2015), 303-327, and: Correction to A common generalization of metric, ultrametric and topological fixed point theorems, Forum Math.27 (2015), 329-330
alternative corrected version: (pdf file)
[2] Kuhlmann, F.-V., Kuhlmann, K. and Shelah, S.: Symmetrically complete ordered sets, abelian groups and fields, Israel J. Math. 208 (2015), 261-290
[3] Shelah, S.: Quite Complete Real Closed Fields, Israel J. Math. 142 (2004), 261-272
Colloquium talk at Valladolid, Spain, 2013
Fixed point theorems
(joint work with Katarzyna Kuhlmann) Abstract:
During my joint work with my wife Katarzyna on particular topological spaces that appear in real algebraic geometry ("spaces of real places"), it turned out that already one of the "simplest" such spaces has a very intriguing structure with lots of self-similarities. This led us to the question whether some sort of fractality is around here. But to study fractals, one commonly uses fixed point theorems. For example, Banach's Fixed Point Theorem states that every strictly contracting function on a metric space X has a unique fixed point, that is, there is some x in X such that f(x)=x.
Unfortunately, the spaces we study are not necessarily metric, and their natural topology is not easy to handle. So we wondered whether suitable tools could be borrowed from other, better known settings. In valuation theory, metrics are replaced by ultrametrics (in which every triangle has at least two equal sides and every element in a ball is a center of that ball). The best known example is the p-adic metric. Important principles, like Hensel's Lemma for the p-adics, can be proven by means of ultrametric fixed point theorems. Working with such theorems, I had asked more than 15 years ago the following question: is there a generalization of the ultrametric fixed point theorems in a more topology-like language, that may serve as a common ground for both the metric and the ultrametric world? The answer is yes (and is surprisingly simple). I will report on a very basic fixed point theorem for that works in a minimal setting, not involving any metrics. This theorem not only covers the metric and ultrametric, but also generates a new topological fixed point theorem. The surprise coming with this theorem is that it is not the continuous, but the closed functions that are natural candidates for such theorems.
The key idea that led to the basic theorem was to use the notions "ball" and "spherically complete" from the ultrametric world but to let the balls be given by any collection of subsets you are interested in. For example, in an ordered field, you can take the balls to be the closed intervals. Then "spherically complete" means that the intersection over any chain of closed intervals (ordered by inclusion) is nonempty. From our general theorem one can derive interesting fixed point theorems for such fields. Clearly, the reals have this property, but it is a non-trivial question whether there are any other ordered fields that have it. In a paper in the Israel J. Math. in 2004, Saharon Shelah showed that there are arbitrarily large such fields, which he constructs as unions over ascending chains of ordered fields (a typical logician's approach). In very recent work, we succeeded to characterize these fields and to construct them in one step as power series fields.
As a further application of the basic theorem, fixed point theorems in lattice theory (that have been applied e.g. in computer science) can be proved. For example, the existence part of the Knaster-Tarski Theorem can be derived using the general theorem. We are now investigating how our "ball spaces" fit into these settings, and what the analogues of other results in lattice theory in the ball spaces could be.
Talk at the Conference in honour of Shreeram S. Abhyankar on occasion of his 82nd birthday, Purdue University, July 5-8, 2012
Elimination of wild ramification in immediate valued function fields - continuing Kaplansky's work
Elimination of wild ramification is an important part of local uniformization. In the particular case of an immediate valued function field F|K of transcendence degree 1 it means to find an element x in F such that F lies in the henselization of K(x). (An extension of valued fields is called immediate if value group and residue field do not change.)
This task is trivial if the characteristic of the residue field is 0, and highly nontrivial in the positive characteristic case. In order to prove a theorem of "Henselian Rationality" over suitable valued ground fields K, we need quite a bit of technical preparation, which can be seen as a continuation of Kaplansky's important paper "Maximal fields with valuations I", Duke Math. Journal 9 (1942), 303-321.
In the first step of the proof, we find the element x in the henselization F^h of F. In this step it is essential to know the degree of the extension K(x)^h|K(f(x))^h for polynomials f.
In the second step of the proof, once x is found in F^h, we try to replace it by an element y in F. Here, we need to know the degree of the extension K(x)^h|K(y)^h for arbitrary elements in K(x)^h.
This step can be seen as a special case of "dehenselization", corresponding to the notion of "decompletion" that appears in Temkin's work. Dehenselization in general states that if there is a finite extension F' of F within its henselization F^h such that F'|K admits local uniformization, then so does F|K. Whether this is true is an important open problem. The above special case and Temkin's "decompletion" seem to indicate that the problem could be solved to the affirmative.
One tool in the proofs is to use ramification theory to reduce the problem to considering Galois extensions of degree p, by extending the ground field. Then in the end, henselian rationality has to be pulled down through such ("tame") extensions. This too can be solved within the described framework where criteria are given for the degree of the extension K(x)^h|K(f(x))^h to be 1. Concretely, it can be shown that the trace of a well chosen henselian generator "upstairs" is a henselian generator "downstairs".
Talk at the SECOND INTERNATIONAL CONFERENCE AND WORKSHOP ON VALUATION THEORY , Segovia, Spain, July 18 to 29, 2011
Ultrametrics and Implicit Function Theorems
Talk in the Honorary Colloquium on Occasion of Wilfried Buchholz' 60th Birthday at the Mathematical Institute of the University of Munich, April 4 and 5, 2008:
What is the connection between resolution of singularities and decidability?
Completeness and decidability of mathematical theories are a main subject in model theory. They have been of particular interest in model theoretic algebra. There are nice examples from field theory that by now may well be called ``classical''. Model theoretical results for algebraically closed, real closed and p-adically closed fields have found interesting applications: Hilbert's 17. Problem, Nullstellensaetze, description of positive definite polynomials and their p-adic analogues. In the year 1965 Ax and Kochen generated much interest in model theory through their proof of a correct version of Artin's Conjecture about non-trivial zeros of forms over the p-adic numbers. Since then one of the best known open problems in model theoretic algebra is whether the elementary theory of the field Fp((t)) of formal Laurent series over the field with p elements is decidable. Although this field looks so similar to the field Qp of p-adic numbers and the theory of the latter has been shown by Ax, Kochen and Ershov to be decidable, several excellent model theorists tried in vein to solve this problem. But this is not due to a lack of knowledge in model theory. In contrast to Qp, the field Fp((t)) is a valued field of positive characteristic, and we simply do not know enough about the structure of such valued fields. In this way, model theoretical questions have stimulated new research in a classical area of algebra: valuation theory.
Again in 1965, another famous theorem was proved: Hironaka showed resolution of singularities for all algebraic varieties over fields of characteristic 0. Since then also for this theorem its analogue in positive characteristic has remained an open problem, in spite of all attacks from excellent algebraic geometers. Since Zariski it is known that the local version of resolution of singularities, called ``local uniformisation'', is of valuation theoretical nature. Yet it was a quite unexpected finding that t he decidability problem and the problem of local uniformisation both are based on the same valuation theretical problem: the defect. In the presence of defect, the classification of valued fields up to elementary equivalence, relative to their invariants (value group and residue field), breaks down.
Another good indication for the connection between the two problems is the work of Macintyre and Schoutens. They show that if resolution of singularities in positive characteristic holds, then at least the universal elementary theory of Fp((t)) is decidable.
Talk in the Model Theory and Applications to Algebra and Analysis Programme at the Isaac Newton Institute for Mathematical Sciences, June 2005:
Additive polynomials
I give a survey on additive polynomials, their role in valuation theory and algebraic geometry and what we know and do not know about them. I show their connection with the defect of valued field extensions and the meaning of the defect for the model theory of valued fields and for local uniformization in positive (residue) characteristic. I mention a classification of Artin-Schreier extensions and its applications. I also talk about maximality properties of valued fields and Ershov's notion of extremal fields.
List of open problems and references for this talk: (dvi file) --- (postscript file) --- (pdf file)
Talk in the Workshop on resolution of singularities, factorization of birational mappings, and toroidal geometry at the Banff International Research Station, December 2004:
What can the theory of valued fields say about local uniformization?
The problem of local uniformization can be reformulated as a problem about the structure of valued function fields. I will quickly review this reformulation.
One part of the problem is elimination of ramification. This is harder in positive characteristic because there, you also have to deal with wild ramification, and the main obstacle turns out to be the defect of valued field extensions. I will give examples of non-trivial defect. Then I will show why certain valuations (called "Abhyankar valuations") always admit a positive solution, and describe the valuation theoretical theorems used for the solution.
In order to generalize these theorems, we have to learn more about the defect. A first step is to classify Artin-Schreier extensions with non-trivial defect, which I have done in a recent preprint. Based on this classification, there is joint work in progress with O. Piltant on the higher ramification groups of such extensions. Future work shall also lead to a better understanding of defect extensions generated by additive polynomials other than the Artin-Schreier polynomial.
International Congress on Nonstandard Models of Arithmetic and Analysis at the University of Pisa, June 24 to 28, 2004:
Dense subfields and integer parts
Answering a question asked at the Conference ``Logic, Algebra and Arithmetic'' in Teheran 2003, We show that every real closed (or more generally, henselian) non-archimedean ordered field L admits a proper dense subfield. This is interesting because any integer part of K will also be an integer part of L. If L is ``small'', then L|K must be algebraic. However, there are examples of trdeg L|K being any pre-assigned cardinal. In particular, if the natural valuation on L has no coarsest non-trivial coarsening, then trdeg L|K can be any countable cardinal. At the same time our construction provides a counterexample to the following conjecture: If a valuation v has no coarsest non-trivial coarsening and if the residue field with respect to every coarsening is henselian, then v is henselian. We will also discuss the existence of integer parts and of truncation closed embeddings in power series fields. We show that Boughattas' ordered field which admits no integer part is not henselian. Finally, we show that there is a real closed field that has larger cardinality than the quotient fields of all of its integer parts. It is an open question whether there is a real closed field that is larger than the quotient fields of all of its integer parts, but has the same cardinality.
Seminaire de Structures Algebriques Ordonnees, Univ. Paris 7, France, May 2004:
Classification of Artin-Schreier defect extensions, and characterizations of algebraically maximal and defectless fields
We classify Artin-Schreier extensions of valued fields with non-trivial defect according to whether they are connected with purely inseparable extensions with non-trivial defect, or not. We use this classification to show that in positive characteristic, a valued field is algebraically complete if and only if it has no proper immediate algebraic extension and every finite purely inseparable extension is defectless. This result is an important tool for the construction of algebraically complete fields. We also use the result to show that extremal fields are algebraically complete. A valued field (K,v) is called extremal if for all polynomials f in several variables the value set vf(K^n) has a maximum. Restricting this condition to certain classes of polynomials yields further interesting properties. In that way, we give characterizations of algebraically maximal and inseparably defectless fields. Finally, we give a second characterization of algebraically complete fields, in terms of their completion. As an example by Cutkosky and Piltant shows, a certain property called relative resolution may work with one type of Artin Schreier defect extensions, but not with the other. This connection with algebraic geometry has to be investigated further.
This work was strongly inspired by the first part of Francoise Delon's thesis. Some results are generalized, some others are put in a larger perspective.
Seminaire de Structures Algebriques Ordonnees, Univ. Paris 7, France, April 2004:
Extensions of valuations to rational function fields
We classify all possible extensions of a valuation from a ground field K to a rational function field in one or several variables over K. We determine which value groups and residue fields can appear, and we show how to construct extensions having these value groups and residue fields. In particular, we give constructions of extensions whose corresponding value group and residue field extensions are not finitely generated. One can even construct valuations on rational function fields in two variables which admit an infinite tower of degree p extensions with defect p. Such nasty valuations constitute a serious empediment for local uniformization in positive characteristic, so it is important to study their structure in detail. In the case of a rational function field K(x) in one variable, we consider the relative algebraic closure of K in the henselization of K(x) with respect to the given extension, and we show that this can be any countably generated separable-algebraic extension of K. In the ``tame case'', we show how to determine this relative algebraic closure. These methods can be applied to power series fields and to the p-adics.
Workshop and Conference on Logic, Algebra and Arithmetic at the Institute for Theoretical Physics and Mathematics, Tehran, October 2003:
Additive polynomials and their role in the model theory of power series fields over finite fields and in local uniformization
A polynomial f over an infinite field K is called additive if f(a+b)=f(a)+f(b) for all a,b\in K. If the characteristic of K is 0, then the only additive polynomials are of the form cx with c in K. But if the characteristic is p>0, then for instance, X^p and the Artin-Schreier-polynomial X^p-X are additive. I will explain the particular role that additive polynomials play in the model theory of power series fields over finite fields. This is tightly connected with the structure theory of valued function fields, which in turn also plays a crucial role for the problem of local uniformization. The latter is a local form of resolution of singularities and therefore of valuation theoretical nature. While local uniformization has been proved in characteristic 0 by Zariski in 1940, the positive characteristic case is still open, and only special cases have been solved. In all of these solutions, additive polynomials play a role. Finally, I will sketch some results on the classification of certain Artin-Schreier-extensions of valued fields and their connection with recent work of Cutkosky and Piltant on resolution of singularities in positive characteristic.
Canadian Mathematical Society Summer 2001 Meeting, Saskatoon, June 2-4, Model Theoretic Algebra Session
Additive polynomials and the model theory of valued fields in positive characteristic
Let Fp((t)) denote the field of formal Laurent series over the field with p elements; it carries the t-adic valuation vt. A well known open problem in model theoretic algebra is to find a complete recursive axiom system for the elementary theory of Fp((t)). This would yield that it is decidable. A similar result was shown by Ax-Kochen and Ershov for the p-adics Qp. An adaptation of their axiom system to the case of Fp((t)) is: ``henselian defectless valued field of characteristic p with value group a Z-group and residue field Fp''.
We showed in 1989 that this axiom system is not complete. In 1998 we developed an elementary axiom scheme which holds in maximal valued fields of positive characteristic and describes valuation theoretic properties of additive polynomials on such fields. This axiom scheme is independent of the above axioms. This work has appeared in the JSL. In 1999, in joint work with L. van den Dries, we developed a particularly simple version of this axiom scheme for Fp((t)), using the fact that this field is locally compact. This work is to appear in the Canad. Math. Bull.
Festkolloqium and Conference on Algebra, Model Theory and Theoretical Physics celebrating Rüdiger Göbel's 60th Birthday, University of Essen, February 2001
Functional equations in lexicographic products
(joint work with Salma Kuhlmann and Saharon Shelah)
Let Gamma be a chain (= a totally ordered set), and Delta a chain with distinguished element 0Delta. Given a mapping s: Gamma -> Delta, define the support of s to be the set {gamma in Gamma; s(gamma) not= 0Delta}. The lexicographic power DeltaGamma (in base 0Delta) is the set {s: Gamma -> Delta ; support(s) is wellordered} ordered lexicographically. In DeltaGamma, we denote by 0 the sequence with empty support. We characterize solutions Gamma to the following functional equations: (DeltaGamma)<=0 order isomorphic to Gamma
DeltaGamma order isomorphic to Gamma
(DeltaGamma)<0 order isomorphic to Gamma and discuss cases (and their applications) where such solutions do not exist.
University of Oldenburg, Germany, February 2001
Über das Problem der Desingularisierung in positiver Charakteristik
Im Jahre 1965 bewies Hironaka Desingularisierung für alle algebraischen Varietä:ten über Körpern der Charakteristik 0. Das entsprechende Problem für positive Charakteristik ist bis zum heutigen Tage offen. Es wurde lediglich bis zur Dimension 3 von Abhyankar gelöst. De Jong bewies eine schwächere Aussage ("desingularization by alteration"): hier nimmt man eine endliche Erweiterung des Funktionenkörpers in Kauf.
Der ursprüngliche Ansatz von Zariski ist, zunächst einzelne Singularitäten aufzulösen, und die Lösungen dann zusammenzusetzen. Aber was bedeutet es, lokal zu desingularisieren? Dies führt direkt zum bewertungstheoretischen Begriff der "Stelle". Im Jahre 1939 bewies Zariski mit bewertungstheoretischen Methoden, dass einzelne Singularitäten in Charakteristik 0 immer aufgelöst werden können ("Local Uniformization Theorem"). Für algebraische Flächen in Charakteristik 0 konnte er dann die lokalen Lösungen zu einer globalen Desingularisierung zusammensetzen. Auch Abhyankar folgt diesem Weg, während aber Hironakas Ansatz nicht bewertungstheoretisch ist.
In den letzten Jahren hat der bewertungstheoretische Ansatz wieder an Interesse gewonnen. In meinem Vortrag werde ich zeigen, welche Rolle Hensel's Lemma in der lokalen Uniformisierung spielt, und welche neuen Ergebnisse für positive Charakteristik die Bewertungstheorie liefern kann. Ich werde das bewertungstheoretische Phänomen vorstellen, das für die Schwierigkeiten in positiver Charakteristik (in der Desingularisierung wie auch in der Modelltheorie der bewerteten Körper) verantwortlich ist. Schliesslich werde ich eine Art "bewertungstheoretisches Arbeitsprogramm" skizzieren, mit dem man das Problem der Desingularisierung in positiver Charakteristik neu in Angriff nehmen könnte.
[1] Franz-Viktor Kuhlmann: Valuation theoretic and model theoretic aspects of local uniformization, in:
Resolution of Singularities - A Research Textbook in Tribute to Oscar Zariski.
Herwig Hauser, Joseph Lipman, Frans Oort, Adolfo Quiros (eds.), Progress in Mathematics Vol.181, Birkhäuser Verlag Basel (2000), 381-456
[2] Franz-Viktor Kuhlmann und Peter Roquette:
Abhyankar places admit local uniformization in any characteristic, in Vorbereitung
(dvi file) --- (postscript file)
[3] Franz-Viktor Kuhlmann: Every place admits local uniformization in a finite extension of the function field, in Vorbereitung
Canadian Mathematical Society Winter Meeting, Vancouver, December 2000
On local uniformization in arbitrary characteristic
In 1939, Zariski proved the Local Uniformization Theorem for places of algebraic function fields over ground fields of characteristic 0. Later, he used this theorem to prove resolution of singularities for surfaces in characteristic 0. Apart from Abhyankar's results for dimension up to 3 and de Jong's desingularization by alteration, not much has been known for positive characteristic.
We prove that every place of an algebraic function field F|K of arbitrary characteristic admits local uniformization, provided that the sum of the rational rank of its value group and the transcendence degree of its residue field over K is equal to the transcendence degree of F|K (we call such places Abhyankar places). Further, we show that finitely many such places admit simultaneous local uniformization if they have isomorphic value groups. Since Abhyankar places lie dense in the Zariski space of all places of F|K with respect to the patch topology, simultaneous local uniformization of any finite number of them might open a way to pass from local uniformization to resolution of singularities.
Further, we prove that every place of an algebraic function field F|K of arbitrary characteristic admits local uniformization in a finite extension F' of F. This fact actually follows from de Jong's result. But we can show in addition that F'|F can be chosen to be Galois. Alternatively, F'|F can be chosen to satisfy a valuation theoretical condition which is very natural in positive characteristic. Our proofs are based solely on valuation theoretical theorems, which are of fundamental importance in positive characteristic.
We also indicate certain analogues of our results for the arithmetic case.
[1] Franz-Viktor Kuhlmann: On local uniformization in arbitrary characteristic, The Fields Institute Preprint Series, Toronto (July 1997)
(postscript file)
[2] Franz-Viktor Kuhlmann and Peter Roquette:
Abhyankar places admit local uniformization in any characteristic, in preparation
[3] Franz-Viktor Kuhlmann: Every place admits local uniformization in a finite extension of the function field, in preparation
Model Theory Meeting, Oberwolfach, January 2000
Additive polynomials and the elementary properties of Fp((t))
The abstract is available as dvi file or as postscript file.
[1] Kuhlmann, F.-V.: Elementary properties of power series fields over finite fields, to appear in J. Symb. Logic; prepublication in: Structures Algebriques Ordonnees, Seminaire Paris VII (1997) (postscript file)
Talk at the conference "Model Theory of Henselian Valued Fields", Edinburgh, May 1999
Quantifier elimination and Ax-Kochen-Ershov principles for henselian fields
I shall summarize the Ax-Kochen-Ershov principles and the relative quantifier elimination results which are known for henselian valued fields. Ax-Kochen-Ershov principles are known for the following classes:
henselian fields of residue characteristic 0,
henselian finitely ramified fields (includes formally p-adic fields of fixed p-rank),
tame fields (includes algebraically closed fields and, more generally, algebraically maximal Kaplansky fields).
Tame fields are henselian valued fields K for which the ramification field of the extension K^sep|K is algebraically closed; here, K^sep denotes the separable-algebraic closure of K. The model theory of tame fields has nice applications to the theory of places of algebraic function fields in arbitrary characteristic.
All tame fields are perfect. For imperfect valued fields, not many positive results are known; I shall sketch the problems one encounters when dealing with them. Similar problems appear for fields of mixed characteristic which are not finitely ramified, like certain infinite algebraic extensions of the p-adics.
Relative QE in various forms is known for all above mentioned classes of valued fields, except for the tame fields in general. I shall describe a form of QE which was invented by Basarab [1] and refined by myself [3]. The idea is to show QE relative to a structure naturally associated to every valued fields, which carries more information than value group and residue field. I called this structure ``amc-structure'' since it encodes additive and multiplicative congruences which hold in the field. If O and M denote valuation ring and ideal of K, then the amc-structure (of level 0) is the residue field O/M and the group Kx/(1+M) together with a natural group homomorphism (O/M)x -> Kx/(1+M) whose cokernel is the value group. To cover the case of tame fields (or imperfect fields), one would have to add something which takes care of the structure induced by additive polynomials in the field. At present, there is no solution known for this problem; I shall describe the responsible stumbling block in detail.
For henselian fields of mixed characteristic, one has to use amc-structures of higher level; I shall give their definition. The class of all henselian fields of mixed characteristic admits QE relative to these structures, because they take care of the essential positive characteristic part of the fields. In special cases, one would like to get away with much less complex reducts of the amc-structures. And indeed, the Macintyre power predicates turn out to be such a reduct suitable for the case of the p-adics.
For a summary of QE for the p-adics via cell decomposition (and its use to show the rationality of the Igusa local zeta functions), I recommend [4].
[1] Basarab, S. A.: Relative elimination of quantifiers for Henselian valued fields, Annals of Pure and Applied Logic 53 (1991), 51-74
[2] Basarab, S. A. - Kuhlmann, F.-V.: An isomorphism theorem for henselian algebraic extensions of valued fields, manuscripta mathematica 77 (1992), 113-126
(postscript file) --- [Abstract]
[3] Kuhlmann, F.-V.: Quantifier elimination for henselian fields relative to additive and multiplicative congruences, Israel Journal of Mathematics 85 (1994), 277-306
[4] Pas, J.: Some applications of uniform p-adic cell decomposition, Asterisque 198-200 (1991), 265-271
AMS Annual Meeting, January 1999, San Antonio, Special Session on Model Theory
Local uniformization and the model theory of valued fields in positive characteristic
Recently, it has turned out that fundamental results of valuation theory can be used to prove new theorems in the model theory of valued fields as well as about local uniformization of algebraic varieties; cf. [1]. We sketch these results and indicate how they are used to prove Ax-Kochen-Ershov principles via embedding lemmas. We present our results about perfect valued fields of positive characteristic which were obtained in this way ([2]). We apply them to gain new insight into the structure of the Zariski-Riemann manifold, which links local uniformization to desingularization ([3]). Finally, we discuss the relation between desingularization in positive characteristic and the open problem whether the power series field Fp((t)) (which is not a perfect field!) is decidable. We point out specific aspects of the model theoretic problem that do not appear in the local uniformization problem, and vice versa. E.g., getting rid of tame ramification is essential for local uniformization, but not for embedding problems. Vice versa, local uniformization in positive characteristic (if it exists) would have to be generalized (!) in order to give a solution to our embedding problems. Indeed, we need a relative version which works over non-trivially valued ground fields (where the valuation will in general not be discrete!). We also need additional information about the transcendence basis chosen in the uniformization. This demonstrates that the problems from the model theory of non-perfect valued fields lead to the formulation of very interesting generalizations of local uniformization. However, an example originally given to show that the model theory of Fp((t)) is a hard problem ([4]) also sets a limit to these generalizations.
[1] Kuhlmann, F.-V.: Valuation theoretic and model theoretic aspects of local uniformization, to appear in the Proceedings of the Tirol Conference on Resolution of Singularities 1997 (postscript file)
[2] Kuhlmann, F.-V.: The model theory of tame valued fields, in preparation
[3] Kuhlmann, F.-V.: On places of algebraic function fields in arbitrary characteristic, in preparation
AMS Annual Meeting, January 1999, San Antonio, Special Session on Singularities
A valuation theoretic approach to local uniformization
Using a purely valuation theoretic approach, we have proved a ``valuative version'' of de Jong's theorem. It states that every place of a function field F|K admits local uniformization on a finite normal extension of F ([2]). Our approach has the following advantages:
1) It allows us to prove ``local improvements'': for certain places, only a Galois extension is needed. In special (but important) cases, the place admits local uniformization already on F. Furthermore, instead of asking for normal extensions, one can control the extension of the value group and of the residue field associated to the extension of F ([1],[3]). This is important for certain applications, which we describe briefly. We state our results in detail and discuss the open problems and technical difficulties.
2) It connects the problem of local uniformization in positive characteristic to the open problems in the model theory of valued fields (cf. our talk in the model theory section). We sketch the fundamental valuation theoretic results which we have applied to the problem of local uniformization ([1],[2],[3]) as well as to the model theory of valued fields in positive characteristic: the theory of algebraic valuation independence, Kaplansky's theory of immediate extensions of valued fields, the generalized Grauert--Remmert stability theorem, the structure theory of valued function fields (``henselian rationality''). We indicate analogues of these results in the recent research connected with desingularization.
Finally, we give the definition of relative local uniformization which works with arbitrary valued field extensions. This constitutes an interesting new notion in valuation theory and a nice tool to prove local uniformization results (because it is transitive). We also discuss its connection to ramification theory.
[1] Kuhlmann, F.-V.: On local uniformization in arbitrary characteristic, The Fields Institute Preprint Series, Toronto (July 1997) (postscript file)
[2] Kuhlmann, F.-V.: On local uniformization in arbitrary characteristic I, submitted (postscript file)
[3] Kuhlmann, F.-V.: On local uniformization in arbitrary characteristic II, preprint, Saskatoon (1998)
Colloquium, Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, December 1998
Large Fields
A field K is called "large" if every smooth curve over K has infinitely many K-rational points, provided it has at least one. This notion was introduced by Florian Pop in an Annals paper in 1996. There he deals with problems of inverse Galois theory (a short description will be given in the talk). Among other results, Pop proves a theorem which "approximates" the Shafarevich Conjecture (which states that the absolute Galois group of the maximal cyclotomic extension of the field of rationals is profinite free).
There are several properties of fields which are equivalent to "large". Some of them are tightly connected to my own work of the early 1990's. I state these properties and give an idea of how the equivalence is proved. It turns out that there is a nice relation to properties that origin from model theoretic algebra. These express that K is "existentially closed" in suitable extensions L, that is, every elementary sentence asserting the existence of certain elements will hold in K, provided it holds in L. We show the connection of this notion with the existence of rational points and rational places.
There are many large fields. Basic examples are the algebraically closed, real closed and p-adically closed fields (and then PAC, PRC, PpC fields and fields with universal local-global principles). I explain what "existentially closed" means for the first three examples, by the Nullstellensatz framework.
Finally, I describe a new result about large fields which can be derived in two different ways, either from my results about local uniformization, or from my theory of the space of all (rational) places of an algebraic function field.
Model Theory Meeting, Oberwolfach, October 1998
Rational place = existentially closed?
Take F|K to be a function field and P a place of F which is trivial on K. If FP=K then P is called a rational place. We say that (F|K,P) is weakly uniformizable if there is a model of F|K on which P is centered at a smooth point. The following is well-known: If K is existentially closed in F, then F|K admits a rational place which is weakly uniformizable. For the converse, one has:
Theorem 1: Assume that K admits a henselian valuation w (or, more generally, that K is a ``large field''). Assume further that F|K admits a rational place P.
a) If K is perfect, then K is existentially closed in F.
b) If P is weakly uniformizable, then K is existentially closed in F.
Part b) is well-known. Which places are weakly uniformizable? Local uniformization is not known in positive characteristic, but we can give a partial answer:
Theorem 2 (K. 1997):
Rational Abhyankar places of rank 1 and rational discrete places are weakly uniformizable.
We call a place an Abhyankar place if it satisfies equality in the Abhyankar inequality, i.e., if
trdeg F|K = rational rank vP F + trdeg FP|K,
where rational rank vP F is the rational rank of the value group of P.
If K is perfect and P is a rational place of F|K, then there is a finite extension F|F and an extension of P to F such that P is still a rational place of F|K and (F|K,P) is weakly uniformizable.
Since K is existentially closed in F if it is existentially closed in F, this proves part a) of Theorem 1 via part b). For vP denoting the valuation associated with P, and vPow its composition with w, we demonstrate that a certain kind of existential sentences which hold in (F,vPow) will also hold in (K,w) (although in general it cannot be expected that (K,w) be existentially closed in (F,vPow)). To prove this by an embedding lemma, we use a result about the density of certain ``nice'' places in the space of all rational places of F|K, with respect to an ``existentially constructible topology''. Part b) of Theorem 1 can be proved in a similar way, also in the case of large fields.
Back to Franz-Viktor Kuhlmann's Home Page
Link to The Valuation Theory Home Page
Last update: April 11, 2016


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Metro & state: 3 U-M, 1 CMU wrestler earn All-America honors
The top eight grapplers in each category earned All-America honors.
Metro & state: 3 U-M, 1 CMU wrestler earn All-America honors The top eight grapplers in each category earned All-America honors. Check out this story on Freep.com: http://on.freep.com/1Rc0wTL
Michigan Published 1:19 a.m. ET March 20, 2016
Ohio State's Nathan Tomasello, top, grapples with Michigan's Conor Youtsey in a 125-pound match during the Division 1 wrestling championship in New York, Saturday.(Photo: Seth Wenig AP)
Wrestling: Three U-M wrestlers and one from Central Michigan attained All-America status at the NCAA championships Saturday at New York. Michigan's Adam Coon was third at heavyweight, Alec Pantaleo placed sixth at 149 pounds and Conor Youtsey was fifth at 125. CMU's Justin Oliver was seventh at 149 pounds. The top eight grapplers in each category earned All-America honors.
Baseball: Wayne State completed a three-game sweep of St. Michael's with a 4-1 win at Auburndale, Fla. It was the fourth straight victory for the Warriors (7-7). Starter Chris Horvath (1-3) picked up the win. He pitched six innings, allowing one earned run on four hits and striking out eight. Wayne State opens at home with a doubleheader Friday against Hillsdale.
Women's tennis: Michigan beat host Michigan State, 5-2. Ronit Yurovsky, Brienne Minor and Mira Ruder-Hook won at singles for U-M (8-4). Athena Trouillot and Emily Meyers won singles matches for the Spartans (8-5).
Men's lacrosse:Dominic Hamper scored 1:49 into overtime to lift host Albion over Aurora,14-13. David DiRado tied the game with 53 seconds left to send it into the extra session for the Britons (1-4).

redpajama_set_name: RedPajamaCommonCrawl


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Sabres' Evander Kane pleads not guilty to charges in N.Y. bar incident
BUFFALO, N.Y. (AP) — Buffalo Sabres forward Evander Kane pleaded not guilty Monday to charges alleging he grabbed three women during an altercation at a downtown bar in June.
Kane didn't speak as his attorney entered the plea for him in Buffalo City Court during the brief appearance. Judge Barbara Johnson-Lee scheduled his next court date for Sept. 9.
Kane, who turns 25 Tuesday, was arrested July 22 after turning himself in to police. He was charged with non-criminal harassment, disorderly conduct and trespass and was released after being processed.
The charges stem from an alleged incident that occurred early on June 24 at Bottoms Up, a nightclub in Buffalo's popular Chippewa Street entertainment district. Three women said they were grabbed by Kane inside the bar. A male bar employee said he also had a run-in with the NHL player.
Reports: Evander Kane arrested for June incident at Buffalo bar
His lawyer, Paul Cambria, has questioned why Kane was charged with trespassing when he was invited to the bar by its owner. Cambria called the allegations "extremely exaggerated" while saying his client "denies strenuously any wrongdoing."
Cambria also played down reports that some of the encounters were captured by the bar's video surveillance cameras.
Erie County Acting District Attorney Michael Flaherty said, "it's our opinion that the evidence does support the charges," but wouldn't go into details about what the video showed.
According to the complaints given to police by the three women, Kane either pulled their hair or grabbed them by neck during encounters inside the bar. One of the women said Kane told her, "You're coming to my house with me and you're going to like it."
When the woman told him no, Kane grabbed her around the neck with both hands, the woman told police.
Another woman told police that Kane grabbed her hair from behind, while the third said he grabbed her throat and pulled her hair.
A bouncer told police that the DJ sent him a text around 3 a.m. saying, "Kane's gotta go." The bouncer said that after he told Kane he had to leave the nightclub, Kane pushed him twice before "someone else grabbed Kane and walked him out the back."
After the bar closed, employees watched video surveillance that showed Kane grabbing one of the women by the throat on the dance floor, the bouncer said.
In March, prosecutors announced that Kane would not face a sexual assault charge stemming from a December incident in Buffalo because there was no evidence to support the allegation.
The fourth player selected in the 2009 draft, Kane was acquired in a multiplayer trade with Winnipeg in February 2015. He scored 20 goals and added 15 assists in 65 games last season. He has two years remaining on his contract.


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BERLIN — A lawmaker from the far-right Alternative for Germany party was attacked and seriously wounded by several men in the northwestern city of Bremen in what police said Tuesday may have been a politically motivated assault.
The beating of Frank Magnitz, a lawmaker in the national parliament who leads the party's branch in Bremen, drew condemnation from across the political spectrum.
"There's zero tolerance for violence, whoever is affected and wherever the violence comes from," German Interior Minister Horst Seehofer told The Associated Press.
Police said the 66-year-old Magnitz was beaten over the head with an unidentified object by at least three men in dark clothing and hoods or hats, who then fled. Two workers loading a car nearby found him on the ground and called an ambulance.
Magnitz was hospitalized, and he told the dpa news agency that doctors want him to remain there until the weekend. He said he had little memory of the attack.
His party, known by its German acronym AfD, distributed a photo of him lying on a gurney, with a bloody, gaping wound on his head and his right eye bruised and swollen.
Authorities appealed for witnesses to the attack, saying they're investigating whether Magnitz was attacked because of his political work, but haven't ruled out other possibilities.
The AfD said Magnitz was ambushed after leaving a newspaper's New Year reception, beaten unconscious with a piece of wood and then kicked in the head as he lay on the ground.
"It was clearly an attempt to murder Mr. Magnitz," AfD co-leader Alexander Gauland told reporters in Berlin.
"This is the result of the ostracism and agitation AfD faces," he said, suggesting other German political parties were partly responsible for the attack because they had compared AfD to Adolf Hitler's Nazi party because of its nationalist rhetoric and campaigns against migrants.
Magnitz told dpa that while he had received threats, he hadn't considered any of them concrete.
The party claims there have been "hundreds" of attacks against its officers and members since its founding in 2013.
Last week, an explosion outside one of its offices in the eastern town of Doebeln damaged windows and doors.
Magnitz is associated with the extreme right faction of the party, including its firebrand leader in the eastern state of Thuringia, Bjoern Hoecke.
Bremen, Germany's smallest state, has a regional election on May 26, the same day as the European Parliament elections in which AfD hopes to make gains.
"There is no justification for this," Maas said, calling for those responsible to be punished.
That was echoed by other politicians from established parties, including prominent Green party politician Cem Ozdemir, who said AfD must be countered by legal means, not violence. "Anyone who fights hatred with hatred always lets hatred win in the end," he tweeted.
AfD is represented in all of Germany's 16 state parliaments. It entered the national parliament in 2017 and is the biggest opposition party there. It views the country's established political parties with contempt, and the feeling is mutual.
The party won 10 percent of the vote in Bremen in the 2017 national election, below its nationwide result of 12.6 percent. Bremen is not considered an AfD stronghold, unlike three states in Germany's ex-communist east that hold regional votes in September and October.
Germany has seen other attacks on politicians in recent years.
In 2015, a leading candidate for mayor in Cologne was stabbed in the neck by a far-right extremist. Henriette Beker, who was in charge of housing refugees when she was stabbed, was elected mayor the following day while still in an induced coma and took office about a month later.
In 2017, a man with a knife attacked the mayor of Altena in western Germany. The mayor was known for voluntarily taking in more asylum-seekers than the small town was obliged to do so by authorities.


2013-2014 Postdoctoral position at the Institute for Mathematics, Astrophysics and Particle Physics of the Radboud University Nijmegen in The Netherlands, working on chemical abundances of stellar populations and semi-numerical neutrino fluxes in correlation with GRBs.
2012 Visiting astronomer at the Institute for Mathematics, Astrophysics and Particle Physics of the Radboud University Nijmegen in The Netherlands, working on GRBs and their connection with neutrinos.
2011 Postdoctoral position at the department of Physics and Astronomy of the Utrecht University in The Netherlands, working on Globular Clusters in M31 and theoretical neutrino fluxes from GRBs.
2007 Postdoctoral position at the department of Physics and Astronomy of the Utrecht University in The Netherlands, working on spectroscopic and photometric analysis of Globular Clusters in M31.
2005-2006 Unpaid leave - Family / health related.
2003-2005 Post-doctoral associate at the European Southern Observatory (ESO) in Garching, Germany, working on study of GRB light curves, and photometry and astrometry of AO images of very crowded fields (Galactic globular clusters).
2002 Post-doctoral researcher at the Center for Adaptive Optics (CfAO) at the University of California at Santa Cruz, working on photometry and astrometry analysis of AO images of very crowded fields (Galactic Center).
2001 Visiting post-doctoral researcher at the Center for Adaptive Optics at the University of California at Santa Cruz.
1997-2000 PhD student at the Max Planck Institute for Radio-Astronomy and University of Bonn, studying GRB analytical modeling and origin of UHE cosmic rays and neutrinos.
1993-1997 Undergraduate student first at the University of Bologna (master in astronomy) and later on at La Sapienza University in Rome (master in physics), studying detection of elementary particles (magnetic monopoles and neutrinos) at the National Laboratories of Gran Sasso in Italy.


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*Photo Credit: Ashley Graham, CC BY 3.0 via Wikimedia Commons
Ibtihaj Muhammad
US Olympic Medalist, Entrepreneur, Activist & First American Woman to Compete in the Olympics in hijab
RELATED TOPICS: Asian Speakers, Civil Rights & Social Justice, Design & Fashion, Humanitarian & Philanthropy, Mental Health, Olympian, Women's Equality, Workplace Diversity, Youth Advocacy
As a young athlete, Ibtihaj struggled with the restrictions wearing a hijab imposed on the requisite sport uniforms, until she discovered fencing, where she finally felt she could be true to herself. She went on to attend Duke University, where she was a three-time All-American and the 2005 Junior Olympic Champion. A member of the U.S. National Fencing Team, Ibtihaj jousted her way into the history books at the 2016 Summer Olympics in Rio de Janeiro wearing her hijab, ultimately helping the women's fencing team earn the bronze medal. As a stereotype-busting trailblazer and inspirational role model, she is an official sports ambassador, serving on the State Department's Empowering Women and Girls Through Sport Initiative and talking with young women around the world about the importance of sports and education. Drawing from her triumphant journey and unwavering commitment to her authentic self, Ibtihaj inspires others to overcome any obstacle and pave their own unique path to success.
Ibtihaj Muhammad is an entrepreneur, activist, speaker and Olympic medalist in fencing. A 2016 Olympic bronze medalist, 5-time Senior World medalist and World Champion, in 2016, Ibtihaj became the first American woman to compete in the Olympics in hijab. Ibtihaj was a 3-time All American at Duke University where she graduated with a dual major in International Relations and African Studies. In 2014, Ibtihaj launched her own clothing company, Louella, which aims to bring modest, fashionable and affordable clothing to the United States market. In 2017, Mattel announced their first hijabi Barbie, modeled in Ibtihaj's likeness, as part of Barbie's "Shero" line of dolls. The Barbie became available for purchase in July 2018. Ibtihaj released her debut memoir in July 2018, PROUD: My Fight for an Unlikely American Dream. Ibtihaj released her third book, children's picture book, The Proudest Blue: A Story of Hijab & Family, that became a New York Times' Best-Seller.
Ibtihaj is a sports ambassador with the U.S. Department of State's Empowering Women and Girls through Sport Initiative, and works closely with organizations like Athletes for Impact and the Special Olympics. Named to Time Magazine's 100 Most Influential list, Ibtihaj is an important figure in a larger global discussion on equality and the importance of sport. Her voice continues to unite both the sports and non-sports world.
Ibtihaj worked with NBC during the 2020 Tokyo Olympics, broadcasting 62 fencing matches. She has also been an outspoken advocate to push the International Olympic Committee into changing their rules/regulations to be more equal (Rule 50, etc.)
A Conversation with Ibtihaj Muhammad
Muhammad speaks regularly in keynote, fireside and panel formats around a range of topics including diversity and inclusion, technology, leadership, activism, overcoming obstacles, entrepreneurship, fashion and beauty.
Contact Ibtihaj Muhammad for an appearance by reaching out to Key Speakers at (949) 675-7856, or by leaving an inquiry.
Jackie Joyner-Kersee
Three-Time Olympic Heptathlon Gold Medalist, Widely Regarded as "The World's Greatest Female Athlete"
Travels From: Missouri
Minda Harts
Women in Business Speaker, Career Revolutionary
Richard Lui
MSNBC-CNN Anchor, AARP Caregiving Champion; Gender Equality Activist; Philanthropist
Two-Time Emmy Award-Winning Television Anchor; Anchor of Inside Edition


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ColumnsTurn Order
By Edwin "Lupe" Moriarty
Credit: Modiphius / Bethesda
At the start of The Elder Scrolls: Skyrim, the player arrives in the game in shackles, as a slow cart meanders its way through mountainous terrain. NPCs with dubious voice acting bicker as you ride forward, and the game scrambles to establish the key story beats in a few precious seconds. Stormcloaks, Imperials, High King, Helgen, all of these ideas are thrown at you in a lump, and then you're dumped out the other end to stop and fiddle with appearance sliders for half an hour. It's only once you've had your execution interrupted and you can flee the burning city that the game really begins. Well, not really, it's more that the game really begins when you find and kill your first dragon and get your first shout. I think. It's hard to tell.
Skyrim is a game with a lot of false starts, and where as a player you spend an awful lot of time not doing much before you get to do anything really cool. It's very much the Fallout 3 problem, and it's notable that there are plentiful popular mods to let you skip the opening.
When I tell you that The Elder Scrolls: Call to Arms is a painfully faithful recreation of Skyrim in tabletop form, you should understand it in that context. Skyrim is a beloved game that millions of people have spent hundreds of hours exploring and enjoying. So too in TES:CtA is there a fascinating, crunchy, exciting game, but just like with Skyrim it's walled up behind a painful slog to get to the interesting stuff. The end result is a game that it's hard to recommend to anyone except the most die hard Skyrim fans, because only they are likely to have the patience to push through.
First Steps to Adventure
The Elder Scrolls: Call to Arms is a tabletop miniature game that can be played competitively by two people (in battle mode) or cooperatively or as a solo game (in delve mode). It's produced by Modiphius Entertainment—who also make the Fallout miniatures game we reviewed—as well as roleplaying games like Star Trek Adventures and Achtung Cthulhu. It's designed for play with a handful of miniatures controlled by each player, with some wandering monster miniatures appearing. This puts it firmly in the skirmish scale category and it's played with 32mm scale miniatures with relatively realistic proportions (making them skinnier and a little taller than Games Workshop products).
The product selection is a little unusual, and you'd be forgiven for assuming (as I did before it arrived) that the core rules box included miniatures and enough stuff to play; unfortunately this isn't the case. The beautifully made, dense, heavy box of rules is literally just the rules. Tokens, cards, a paper battlemat and three rulebooks make up this package. It's a huge mountain of stuff, more akin to the accessories you find in a lavish kickstarter boardgame (and we'll come back to that later).
The miniatures themselves you have to buy separately, and that's… a bit rough. You basically need the Bleak Fall Barrows Delve set to even play the tutorials, so you're going to have to pick that up. But that's not actually enough to play a battle game, so you'll also probably want to grab some Stormcloaks and Imperials too. That makes the "starter bundles" that Modiphius sell with a rules box and the three most basic minis boxes included a sensible purchase but the price tag… well, we'll come back to price later. The miniatures are also available in plastic and resin, and while I didn't get any of the plastic miniatures provided to review, it's clear from other reviews and from the Fallout minis that we received that their quality is not fantastic. The resin miniatures on the other hand, are absolutely stunning but… well, we'll come back to that too.
If you head over to the Modiphius store you might notice that Escape from Helgen (the tutorials) and the core rulebook are available as free PDF downloads, with the Quests (scenarios) being a download that costs the same as a fancy coffee. There's even a print and play file for the custom dice. You might even grab some minis and think that means you can get playing right away but… no, you can't. Because the entire game revolves around the plethora of cards, and those are only available in the core rules box. So you're going to have to splash cash on that to even just play the tutorial.
So let's assume you have your Bleak Fall Barrows Delve set and the rules. Now we hit some good news, actually some great news. The Escape from Helgen tutorial booklet is absolutely fantastic. It's a series of three linked tutorial scenarios using literally just a couple of miniatures, with premade decks. Each one teaches you some core concepts, introducing more and more of the game in each of the tutorials. By the end of the booklet—which doesn't take more than an hour to set up and play through—you'll have the basics down of how checks work, how you move, what actions you can do, what the most important bits on each card do, and so on.
It's hard to fault this as a tutorial packet – it's evocative, narrative, well-paced and easy to read and play with. At the end there's a little quick reference page which I continued to use the entire time I played. It also concludes with the words
"When all the tutorials are complete, it's time to open the core Rulebook. You are now ready to learn the full rules."
Which marks the point where the onboarding process of the game really falls down.
A Slightly Too Open World
When you look at the rulebook itself you might be forgiven for thinking that it's actually not too intimidating – after all, many wargames have a huge rulebook! This one is little, a half size paperback with only about 100 pages. Surely this will be a breeze, after all we just played through the tutorials.
What you've not realised if you have these thoughts is that this little book is absurdly dense. First of all, unlike many rulebooks there is effectively no background or lore material of any kind—it's assumed you know what the setting is. This is a good indication of their target market in many ways. The game always presumes that you have played Skyrim and know what The Elder Scrolls is as a setting, and doesn't spend any time explaining it to you. But that means that all 100 of those pages are rules.
Another way that these books can often end up looking lengthier than they are is in the inclusion of lots of spacers – photos, illustrations, chapter splash pages, all that stuff. There's very little of that here; probably less than four full pages of art across the whole book. You might not realise this flicking through though, because the pages are very colourful, packed with lots of diagrams and tables with coloured entries, and custom symbols and all kinds of other visually provocative stuff. That does pose some problems as well however, because with the cramped font, dense text and busy visual style it can feel pretty overwhelming. The best thing I can say about the layout of the rulebook is that the small form factor makes it easy to take places and carry around.
One of the challenges with reading the book is that it doesn't really explain things in a top down way. It opens with giving you some basic information about the components and conventions used, but this quickly devolves into incredibly detailed and dense descriptions of all the element of a character card, or an upgrade card, and these are not simple components. We make it through here and we get to the skill test, and how that works… but then we stop for an overview of attributes, and then there are modifiers, and substitutes, and effect dice, and there are two half-page tables to explain what the custom dice results mean. It's a brick wall of information, and we're only on page 9 of 101.
If you fight your way through all of this though, you remember that… you've already played the tutorial! You know this already! Right? Well, mostly. One thing that the tutorial does well is give you a sense that you know what's happening, but one thing it does badly is mislead you into thinking that means you know what's happening in the game proper. Sure, the basics are the same, mostly, but there's so much stuff in the core rules that it's hard to tally the tutorial with them.
One of the biggest complaints of Skyrim is that it sometimes felt too big: too many options, too little direction. Lots of people loved that, wandering off, making their own fun, finding things in the world that weren't the main quest, but others felt frustrated or overwhelmed at the sheer scale of options. Call to Arms replicates this sensation faithfully. There's just so much stuff in this game to get to grips with. This is a miniatures game with 5 attributes and 19 skills, with skills having a plethora of associated perks. Some of them have upwards of 15, and even the leanest has half a dozen. Each of these is a rule, listed in block text, that you have to reference. They're not listed on the character cards. You have to know what the perk is and what the symbols mean and look them up.
You can do almost anything in this game that you can do in Skyrim, but that is actually a huge problem. The open nature of the game, the huge number of possibilities, will excite and thrill some players, but overwhelm and frustrate others. As a veteran of dozens of wargames, complex and simple, I found my head spinning at the sheer amount of stuff on offer. But if the idea of having a character who can smith an axe, enchant it, block a hit with a shield, then instantly eat a wheel of cheese to regain fatigue all in the game appeals to you… this is probably a plus, not a minus.
A Slightly Too Empty World
Now we've established that Call to Arms has a wild abundance of toys to play with, it's time for us to look at if doing that is actually fun.
Those 19 skills don't actually all tie into actions – just like in the video games, some of them (like light and heavy armor) are more permissions and buffs than anything else. Light Armor "allows the model to fight while wearing Light Armor" and that's a pretty good description of what it does. Others are actually tied to specific actions, like lockpicking and block. These all have their own rules, kept with the other more generally accessible rules, and these are probably the best skills in my opinion – they give you more cool stuff to do. Equally, the magic skills let you cast spells, and that's great, though they are much less available than it feels like they are when you play the video games, because you can't dip your toes as easily into them.
Magic is of various flavours (alteration, conjuration, destruction and illusion in the core book) and spells cost magicka to cast from a pool. There are a variety of different ways of targeting them, and some specific subtypes of spell. I like these specific types the best, perhaps, but it's probably not necessary to go over them in detail on the grounds that these are the spells in the videogames. They work in basically the same way, have the same strengths and weaknesses, and do what you expect.
Dragon Shouts are another completely faithful adaptation of the video game lore. It feels oddly niche to include a whole system for something that literally one character in the game can do, but I guess you gotta hit that licensing button as hard as you can when you snap up something like this. They're fine, but again they do what you think they would, and mechanically work basically exactly like spells but without a magicka cost (they cost a currency called Thu'um instead).
Now we come onto perks, and holy crap there are a lot of perks. You can be a sneaky character who is sneaky with daggers, or with bows, or that can walk over traps without setting them off, or which make it harder to hear them when they're walking, or which can run away really well, or… you get the idea. Every single one of these things is a perk, and I haven't listed all the effects by a long shot and that's just one skill. Sneak doesn't even have the most perks, not by a fair way!
There are so many of these and they can basically be broken down into two categories:
Let you do a thing you couldn't do, or gives you a special rule you couldn't normally have
Gives you a bonus or your opponent a penalty
That's it. There are not exciting subsystems, or new play opportunities. You want to be really good at sneak, and take all the perks? You'll be able to hide really well and move fast when you're hidden and your opponents will not be able to hear you and you'll be really good at sneak attacking in a bunch of ways. And that's it. Which is cool, but it feels a little flat – the basic rules cover everything, and these little buffs and changes definitely make characters different, but I never felt joy at my character's perks. I never went "Oh yes, I have x!" like I do in some games. I spent a lot more time going "Oh, I've rolled the wrong dice on that test, because I have [insert four different perks here]".
So we have this dizzying array of not hugely interesting rules and oh no you thought we were done we're not done. Not by a long shot. Because this is Skyrim I mean The Elder Scrolls and this game is going to faithfully reproduce everything in there whether you want it to or not. That means racial bonuses, that means equipment, potions, food, money if it's in the video games, it's in here. Every single one of these things has rules, and options, and the cards mostly just tell you the name of the thing and expect you to remember or look it up every time.
Here's a character card for Hadvar, with upgrades in tow:
It's a lot of stuff
Now this is probably the most complex looking card you'll have in your party – less important models get less stuff, but they all get stuff and just look at how much stuff is on Hadvar's card! It's overflowing with stuff. And this isn't the most complicated a card can get – there are characters with special rules, more perks, more skills, all kinds of stuff.
And you can see here as well how the symbols and notations don't help at all. Persuasion, Sword and Board, Nord, Frost Resistance, the little picture of a bow and the little picture of a lockpick, they all do stuff. They all have rules. Rules that I found myself looking up again and again. And so much of it basically amounts to "Oh I should have rolled an extra die on that test".
One of the major criticism of Skyrim was that it had this huge sprawling world, and it all felt very empty. It often felt like the same town copy-pasted again and again, to give the illusion of space and complexity, without really following through on much of it. In this way as well, Call to Arms is very much an authentic adaptation. Again, for many people they didn't care and they won't here either. Lots of people get a real thrill out of counting up all the dice to roll, and pooling all your cool bonuses to get to win out, and if that's you, you're going to love this. If it's not, then you're going to feel pretty exhausted by the entire affair, this huge hill to climb to find at the top there's mostly more hill.
Comrades in Arms
One of the big appeals to me about this game was delves. Battle mode plays out a lot like most wargames – you have a bunch of scenarios, you have deployment zones, you're trying to attack each other and that's basically it. There's an interesting twist in that you might have some random baddies wandering around, and often you're attempting to contest exploring something or taking some treasure, but ultimately it's the kind of fare you've seen before.
Delves on the other hand are something more unusual – a true cooperative or solo enterprise. I don't want to bury the lead here, so I'll say right up front that this is the most responsive, most challenging and most consistently playable adversary system I've seen in a miniatures game. At no point did I feel like I didn't know what to do with the enemies, and they acted in what felt like plausible, challenging ways. I really enjoyed my solo games, and a big part of that was the adversary system.
Now the bad news. The system accomplishes this by doing what it does in every other part of the ruleset: stuff. In this case, the stuff is mostly flow diagrams.
I don't want to make it seem like I think this is a bad solution – it's not. The diagrams were helpful, and really helped modulate the game. But there are a bunch of them, for lots of different situations, and the rules for antagonists are one of the meatiest parts of what is a very protein rich book. I certainly wouldn't want to try and play them with someone who wasn't an experienced gamer, or whose tolerance for stopping and looking things up was low.
That said, when I got the hang of it, it was really good. It felt more organic and realistic than other systems, and soon I was slapping draugr with swords and nicking their stuff, and it felt pretty fun. As a coop game it's also a nice addition – I haven't quite convinced my husband to play with me, but I'm definitely planning on roping in some boardgaming friends when lockdown lifts to give it a spin.
Overall, if you buy this game as a solo or coop project, that might be the way to do it. On your own you're not waiting for other people to puzzle out what their models do. And played cooperatively you can help each other out navigate the jankier elements of the rules, and get things playing more smoothly. This really feels like how the game was supposed to be played, and it makes sense that Modiphius have consistently given it equal top billing, and not pushed the competitive angle too hard.
Modelling Adventure
Credit: Lupe
In my big exciting box from Modiphius I was provided with the Resin Starter Bundle – that's the Delve set, Stormcloaks and Imperials, all cast in high quality resin. I'm going to talk about them altogether because these are honestly some of the most consistent resin miniatures I've seen in terms of quality, and there's little to pull apart between the sets (this is a good thing).
First of all the casting quality is absolutely stunning. I've only ever had resin miniatures this good from Atlantis (which, it turns out, uses the same caster), and those are my go to recommendation for people who aren't sure if resin can be a good material for minis. The detail is crisp and fine, the casting is excellent, with minimal flash or slip. The pieces, once washed and cleaned up just a little, were ready for spraying without almost any fuss, and come as a couple of pieces in most cases.
The detail on these is absolutely breathtaking. As a technical sculpting and casting enterprise, I've rarely been more impressed—these are some of the best miniatures from a pure quality standpoint I've ever worked with. They are so intricate and perfect that I found myself intimidated by the sheer task of doing them justice.
Which leads into one of the major negatives about them: they are too complex in some ways. As a veteran painter who doesn't baulk at many tasks, I was absolutely overwhelmed by the detail on these. Each model was a serious undertaking, and there are few good easy surfaces that take washes well and give you a break. Every part needs careful, considered painting and detailing to really make it shine. I play every day and it was a challenge; for a new hobbyist I imagine it would simply feel impossible. It's difficult to know who these are for, because they feel like the best possible quality display resins, but equally you need a bunch of them and the IP feels best geared to drawing in people who wouldn't normally play minis games.
As I didn't receive the plastics I can't comment directly, but the issues with Modiphius' plastic miniatures are well documented (including on Goonhammer), and the sculpts will remain the same, so I don't see them getting easier to paint.
I'm thrilled to own these miniatures, and I'm very pleased with how they look painted up, but they were an enormous time and effort sink, and I can't say I plan to pick up any more, even just as a hobby project.
Victory… but at what cost?
So we can conclude that Call to Arms is a complex, labyrinthine, vast miniatures game offering an insane array of possibilities. It is probably the most faithful adaptation of an IP I've ever seen in a game, offering you the ability to mimic the play of Skyrim in particular almost exactly. It feels like the videogames it's based on which is a real achievement.
Unfortunately, the big market of "people who really like Skyrim" that might be tempted to pick it up are likely to be put off by the complex detailed miniatures, the vast number of rules, and the uphill struggle to learn what everything does.
For people who are gamers first, I can really recommend this if you want something crunchier and more "minis games" than what most coop dungeon crawler boardgames can offer, but probably not for any other reason.
The true market is the small slice of the piece which is "people who really love Skyrim even a decade later" and "people who are really into miniatures games and don't sweat a lot of complexity". If that's you, then I cannot recommend this game more – you will absolutely adore it. But for anyone else? It's a hard sell, particularly because of the price tag.
If you want what I got, the Resin Starter bundle, you're looking at £115, and that's a big wedge of cash for what is, out of the box, surprisingly limited. You can't really do full sized battles with just that starter. Looking at what I'd want to play this competitively I totalled up another £70 at the very least, and really you want to spend another £70 on top for the extra stormcloak and imperial boxes… that aren't even out yet. Oh, and to play with those you'll need another card set and expansion, and that costs money too.
In the end then, this is a game for people who are dab hands with games, loved Skyrim, and don't mind blasting money like a firehose now and in the future. That's a tough sell for me, but if you're in the position to drop a lot of cash and Skyrim is one of your touchstone properties, I can definitely see why you'd jump at it.
A review copy of the materials covered in this article were provided by Modiphius.
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With its gently tapering handles and sculpted silhouette Aria is a resolutely modern design with tactile appeal. Featuring the unique GROHE StarLight® chrome finish, the soft organic body leads to the ergonomicallydesigned handles, which benefit from Carbodur head parts for smooth and long lasting operation.
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What Is the Perfect Book in the Bible for Those Who Are Afraid?
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As much as we would like to say we have Covid-19 all figured out it's ok to admit that we don't. Let us encourage you as we walk through these difficult days together.
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Where is my life headed?
Fear and uncertainty are running rampant in our world today.
The Coronavirus (COVID-19) pandemic, politics, global conflict, natural disasters and many other events are making many people feel uneasy and anxious about the future. Some people have completely lost hope. Is there a book in Scripture that could help encourage us during this time of crisis?
Although this may sound strange to some, I suggest that you read the book of Revelation if you are feeling fearful today.
The book of Revelation tends to make people nervous. There's a lot in there that we can't wrap our minds around. Consequently, Revelation is often read with some measure of fear and uncertainty. Alternatively, some Christians (including pastors!) ignore it altogether.
But at its core, Revelation is a book of hope that's extremely relevant to our lives today because it lays out in detail what the future holds.
Written by the apostle John, who received the revelation when he was exiled for his faith on the island of Patmos, the book tells us exactly what to expect when Jesus comes again. It's history pre-written — a guide to the signs, circumstances and events that precede and coincide with the return of Jesus.
As Revelation 21:4-5 says:
"'He will wipe away every tear from their eyes, and death shall be no more, neither shall there be mourning, nor crying, nor pain anymore, for the former things have passed away.
"And he who was seated on the throne said, 'Behold, I am making all things new.' Also he said, 'Write this down, for these words are trustworthy and true.'" (ESV)
When Jesus returns, he will do away with all suffering and sorrow. If we are followers of Jesus, that is our future. That is our hope.
Jesus has written the end of our story, and it's an ending that you and I can anticipate with joy! We do not have to face the future with trepidation. Instead, we can face it with confidence.
My prayer is that you'll explore Revelation during these unsettling times and lay hold of the incredible promise that Jesus holds the future — and that includes yours — firmly in his hands. Because when you have confidence that Christ holds your future, you'll not only be empowered to live with hope today, but also to make a difference in this world that lasts into eternity.
John tells us in Revelation 7:9-10,
"After this I looked, and behold, a great multitude that no one could number, from every nation, from all tribes and peoples and languages, standing before the throne and before the Lamb, clothed in white robes, with palm branches in their hands, and crying out with a loud voice, 'Salvation belongs to our God who sits on the throne, and to the Lamb!'"
We carry the promise of a world where Christ wipes away every tear, overthrows every evil, and renews the whole of creation. This is the good news that the world needs so desperately to hear.
And right now, the world needs you and me to shine this light of Christ brighter than ever.
Copyright © April 2020 Jack Graham, used with permission.
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August and September are typically warm and dry in the South Sound. However, this year it has been mostly hot and dry since June. It has been more like Sorrento than the South Sound. Now we can truly boast about our Mediterranean climate. Plants like rosemary, lavender and sage thrive.
Dark green-leaved Rosemary 'Arp', silvery-leaved Lavender 'Silver Frost' and the wide leaves of gray ornamental sage, Salvia 'Berggarten' make a good combination. Throw in a couple of potted red geraniums in terra cotta pots, grab a good book and have a glass of Washington wine. Enjoy our extended new Mediterranean climate.
That's Golden RAIN tree, not Golden CHAIN tree…why these beautiful trees aren't grown more, I'll never know. Koelreuteria paniculata (easier to grow than to say) is blooming now. It has panicles of fragrant yellow flowers and ash-like leaves. The medium-sized tree grows in zones 5-9 in full sun or a little shade. That means it's perfect for the South Sound. The best part about the tree is the fruit that eventually swells into little pink balloons. They make a popping sound when you step on them. Kids love it. Popping fruit may not be the BEST reason to grow this too rarely grown tree but it helps. You can see one up close in Tacoma at S. 11th and Tacoma Ave S. or E. 26th St. near Freighthouse Square. Stunning trees.
Linda Chalker-Scott is our local "mythbuster". Reading her earlier books, "The Informed Gardener" and "The Informed Gardener Blooms Again", gives you a sense of Chalker-Scott's mission…to set us all straight about the science behind our gardening questions…nothing is anecdotal. All of the information in "How Plants Work" is backed up by scientific research.
If you follow The Garden Professors on Facebook you will recognize the Chalker-Scott name. Advice and answers are "no nonsense" to say the least.
"How Plants Work" is Chalker-Scott's referential science for gardeners book. Just like in her previous books, she debunks many of the commonly held "facts" but supports others. She names names and explains why some of the more popular home gardening methods and products simply don't work.
Along with setting us straight about our long-held and at times totally false beliefs about gardening the author provides some very understandable layman's lessons in home gardening botany. She explains the science behind plant growth, water movement, light importance, night bloomers, twining and vining and more.
Timber Press, $19.95, 220 p.
This entry was posted in Book Reviews, Garden News, South Sound Magazine Article by Vickie Haushild. Bookmark the permalink.


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Tistortiella är ett släkte av skalbaggar. Tistortiella ingår i familjen vivlar.

Kladogram enligt Catalogue of Life:

Källor

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redpajama_set_name: RedPajamaWikipedia


Kazuyo Sejima + Ryue Nishizawa / S A N A A 【募集】設計スタッフ募集しています。 employment_jp(at)sanaa.co.jpまで 【再募集】プレス担当スタッフ募集をしています。 sanaa(at)sanaa.co.jpまで If you want to contact us, please send an e-mail to one of the following addresses.
51n4e 51N4E and Peter Swinnen announced today that Peter Swinnen will be leaving the firm as a partner in order to fully focus on the completion of his State Architect Atelier, the development of a PhD trajectory as well as the establishment of his own architectural platform CRIT . As a founding partner Peter Swinnen has contributed in a profound manner to the work and legacy of 51N4E, which in 15 years' time has established itself as an office voluntarily linking the impact of design intelligence and governance intelligence. Johan Anrys and Freek Persyn will continue to head 51N4E as leading senior partners. The firm's evolving engagement in Europe has recently expanded to Switzerland and Turkey with new projects ranging from strategy to implementation. Peter Swinnen, Freek Persyn and Johan Anrys are looking forward to exchange knowledge and share critical insights as professional independent peers.
lucien pellat-finet Shinsaibashi New Canaan, Connecticut USA 2010.07 Private Residence 830 m2 This is a project in Connecticut (US) to repair a residence designed by Joe Black Leigh, and add a new house to the site. New Canaan is known as a town where many houses from the 1950s by such architects as Philip Johnson and Marcel Breuer still remain, and the one we worked on was the residence for Joe Black Leigh (built in 1956), also a friend of Philip Johnson. Our aim was to inherit the spirit of its beautiful glass architecture, or in other words, the spirit of New Canaan. Cedric Price CEDRIC PRICE (1934-2003) was one of the most visionary architects of the late 20th century. Although he built very little, his lateral approach to architecture and to time-based urban interventions, has ensured that his work has an enduring influence on contemporary architects and artists, from Richard Rogers and Rem Koolhaas, to Rachel Whiteread. Taking the view that architecture should be enabling, liberating and life-enhancing, Cedric Price's approach was all-embracing. From landmark projects such as the 1960-61 Fun Palace, to designs for Christmas tree lights on London's Oxford Street, his projects were governed by the belief that architecture must "enable people to think the unthinkable?. Through projects, drawings and teaching, Cedric Price (1934-2003) overturned the notion of what architecture is by suggesting radical ideas of what it might be.
Junos House Juno's House, Row house in Barcelona Our clients purchased a row house with the intention of doing a modest refurbishment: to renovate the kitchen, opening it to the living room, adding a new bathroom and give the whole a fresher look. When the works began, however, we detected that the quality of construction was extremely poor and that each level was a patchwork of humble materials. The floor slab of the main level almost collapsed on top of us- we then had to come to a halt and analyse the situation.
Rolex Learning Center - SANAA Photo © Iwan Baan The Rolex Learning Center is above all a library and learning space devoted to the cultivation of knowledge by an array of different methods. It has one of the largest collections of scientific literature in Europe, with over 500,000 volumes. In addition, an exciting range of new pedagogical technologies in the building, as well as the layout itself, are innovations to the public's approach to texts and learning. Rolex Learning Center Here is another project of floorly interest. Rolex Learning Center, a project at the Ecole Polytechnique Fédérale de Lausanne in Switzerland , by SANAA, is to create a fluid space for students to enjoy, the description by Patrick Aebischer, President of EPFL, said, "exemplifies our university as a place where traditional boundaries between disciplines are broken down, where mathematicians and engineers meet with neuroscientists and microtechnicians to envision new technologies that improve lives. We invite the public into this space to convey the message that working in science is working for the advancement of society." What is interesting is the morphology of the floors plate.


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MEATGRINDER is a youth oriented resource group and social communion for art in the central Los Angeles area that builds contextual conversations around a place for teens in the art world and vice versa, and is free to join. Originated in the Winter of 2016/2017, MEATGRINDER organizes bi-weekly visits to artists's studios, galleries, museums, as well as art workshops in different mediums and teen art salons.
In June and July of 2017 they were in residence at The Shed Echo Park where they held their first exhibition Something New, Always Better.
For more information you can find them at @meatgrinder.bbqla or email at meatgrinder@bbqla.net.