论文标题
关于普通本地戒指的$ f $ pure-pure阈值的积累点
On accumulation points of $F$-pure thresholds on regular local rings
论文作者
论文摘要
Blickle，Mustaţă和Smith提出了两个猜想，以$ f $ pure的阈值限制。一个猜想询问是否可以将固定尺寸的常规本地环上的$ f $ pure理想阈值的序列写为较低维度的$ f $ pure阈值。另一个猜想预测，正式功率系列的任何$ f $ pure阈值都可以写为多项式的$ f $ pure-pure阈值。在本文中，我们证明了第一个猜想有反例，但较弱的陈述仍然存在。我们还为第二个猜想给出了部分肯定的答案。
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.
