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arXiv · 2001.08923

On accumulation points of $F$-pure thresholds on regular local rings

Kenta Sato
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Abstract

Blickle, Musta\c{t}\u{a} and Smith proposed two conjectures on the limits of $F$-pure thresholds. One conjecture asks whether or not the limit of a sequence of $F$-pure thresholds of principal ideals on regular local rings of fixed dimension can be written as an $F$-pure threshold in lower dimension. Another conjecture predicts that any $F$-pure threshold of a formal power series can be written as the $F$-pure threshold of a polynomial. In this paper, we prove that the first conjecture has a counterexample but a weaker statement still holds. We also give a partial affirmative answer to the second conjecture.

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Kenta Sato. 2020-01-24. On accumulation points of $F$-pure thresholds on regular local rings. https://arxiv.org/abs/2001.08923

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