Finite Generation of Extensions of Associated Graded Rings Along a Valuation

Abstract

In this paper we consider the question of when the associated graded ring along a valuation, ${\mathrm{gr}}_{{\nu }^{\ast }}(S)$, is a finite ${\mathrm{gr}}_{{\nu }^{\ast }}(R)$-module, where $S$ is a normal local ring which lies over a normal local ring $R$ and ${\nu }^{\ast }$ is a valuation of the quotient field of $S$ which dominates $S$. We obtain a very general result in equicharacteristic zero in Theorem 1.5. We also obtain general results for unramified extensions of excellent local rings in Proposition 1.7.

28 pages, Final version

References in corpus (1)

• The role of defect and splitting in finite generation of extensions of associated graded rings along a valuation

Cited by in corpus (1)

• Generating Sequences and Semigroups of Valuations on 2-Dimensional Normal Local Rings