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

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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 thresshold 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.

Original languageEnglish
Pages (from-to)614-635
Number of pages22
JournalJournal of Algebra
Publication statusPublished - May 15 2023

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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