Toroidalization of generating sequences in dimension two function fields

Details Toroidalization of generating sequences in dimension two function fields Toroidalization of generating sequences in dimension two function fields

2005-09-29

arxiv.org/abs/math/0509697v1

Mathematics

Commutative Algebra

28 pages, to appear in J. of Algebra

Scientific paper

Let k be an algebraically closed field of characteristic 0 and let K*/K be a finite extension of algebraic function fields of transcendence degree 2 over k. Let v* be a k-valuation of K* with valuation ring V* and let v be the restriction of v* to K. Suppose R --> S is an extension of algebraic regular local rings with quotient fields K and K*, respectively, such that V* dominates S and S dominates R. We prove that there exist sequences of quadratic transforms R --> R' and S --> S' along v* such that S' dominates R' and the map between generating sequences of v and v* in R' and S', respectively, has a toroidal structure. Our result extends the Strong Monomialization theorem of Cutkosky and Piltant.

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