2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65981Suppose 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.50 pagesAlgebraic GeometryCommutative Algebra14B05, 14E05, 13A18, 13B10text