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

DOI10.1016/J.JALGEBRA.2023.02.010arXiv2001.08923MaRDI QIDQ6333423

Publication date: 24 January 2020

Abstract: Blickle, Mustac{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.

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Positive characteristic ground fields in algebraic geometry (14G17)

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