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Ascending chain condition for
$F$-pure thresholds on a fixed strongly 
$F$-regular germ
- Part of
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- Journal:
- Compositio Mathematica / Volume 155 / Issue 6 / June 2019
- Published online by Cambridge University Press:
- 28 May 2019, pp. 1194-1223
- Print publication:
- June 2019
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- Article
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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.
