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arXiv · 1704.05713

Finite Generation of Extensions of Associated Graded Rings Along a Valuation

Steven Dale Cutkosky
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Abstract

In this paper we consider the question of when the associated graded ring along a valuation, ${\rm gr}_{\nu^*}(S)$, is a finite ${\rm gr}_{\nu^*}(R)$-module, where $S$ is a normal local ring which lies over a normal local ring $R$ and $\nu^*$ 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.

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Steven Dale Cutkosky. 2017-04-19. Finite Generation of Extensions of Associated Graded Rings Along a Valuation. https://doi.org/10.1112/jlms.12120

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