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arXiv 2001.089232020-01math.AGmath.AC

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

Kenta Sato

备注：: 18pages; v2: fixed several typos

英文摘要：

Blickle, Mustaţă 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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