  For a field $F$ and a connected reductive group $G$ defined over $F$, we
develop a theory of Kempf-Rousseau-Hesselink unipotent $F$-strata in $G(F)$
that should allow us to attack open problems in positive characteristic. As an
application, we use this theory to establish the fine expansion of the
unipotent contribution to the (non-twisted) trace formula over a global field
of characteristic $p>0$. The unipotent $F$-strata play here the role of the
unipotent geometric orbits in Arthur's work over a number field. The expansion
in terms of products of local distributions is not discussed here; it will be
the subject of further work.

Representation Theory;Number Theory