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$F$-pure thresholds on a fixed strongly 
$F$-regular germ
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.
