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arXiv · 1710.05331

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

Kenta Sato
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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, Musta\c{t}\v{a} and Smith.

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Kenta Sato. 2017-10-15. Ascending chain condition for $F$-pure thresholds on a fixed strongly $F$-regular germ. https://doi.org/10.1112/s0010437x19007358

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