Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588949 | Journal of Algebra | 2006 | 29 Pages |
Abstract
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 ν∗ be a k-valuation of K∗ with valuation ring V∗, and let ν be the restriction of ν∗ to K. Suppose that 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 and along ν∗ such that dominates and the map between generating sequences of ν and ν∗ has a toroidal structure. Our result extends the Strong Monomialization theorem of Cutkosky and Piltant.
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