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

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