  Suppose that f is a dominant morphism from a k-variety X to a k-variety Y,
where k is a field of characteristic 0 and v is a valuation of the function
field k(X). We allow v to be an arbitary valuation, so it may not be discrete.
  We prove that there exist sequences of blowups of nonsingular subvarieties
from X' to X and from Y' to Y such that X', Y' are nonsingular and X' to Y' is
locally a monomial mapping near the center of v. This extends an earlier result
of ours (in Asterisque 260) which proves the above result with the restriction
that f is generically finite.

Algebraic Geometry;Commutative Algebra