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

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.

28pages; v3: corrected Lemma 2.19; fixed several typos and minor errors; v4: minor changes