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Ascending chain condition for $F$-pure thresholds on a fixed strongly $F$-regular germ

Part of: General commutative ring theory Algebraic groups Local theory

Published online by Cambridge University Press:  28 May 2019

Kenta Sato
Kenta Sato*
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan email ktsato@ms.u-tokyo.ac.jp
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Abstract

In this paper, we prove that the set of all $F$-pure thresholds on a fixed germ of a strongly $F$-regular pair satisfies the ascending chain condition. As a corollary, we verify the ascending chain condition for the set of all $F$-pure thresholds on smooth varieties or, more generally, on varieties with tame quotient singularities, which is an affirmative answer to a conjecture given by Blickle, Mustaţǎ and Smith.

Keywords

ascending chain conditionF-jumping numberF-pure thresholdtame quotient singularitiesnon-standard extension

MSC classification

Primary: 14B05: Singularities
Secondary: 13A35: Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure 14L30: Group actions on varieties or schemes (quotients)
Type
Research Article
Information
Compositio Mathematica , Volume 155 , Issue 6 , June 2019 , pp. 1194 - 1223
Copyright
© The Author 2019 

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