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

Blickle, Mustata 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.(c) 2023 Elsevier Inc. All rights reserved.