A note on discreteness of $F$-jumping numbers

Abstract

Suppose that $R$ is a ring essentially of finite type over a perfect field of characteristic $p>0$ and that $a\subseteq R$ is an ideal. We prove that the set of $F$-jumping numbers of ${\tau }_b(R;a^t)$ has no limit points under the assumption that $R$ is normal and $Q$-Gorenstein -- we do \emph{not} assume that the $Q$-Gorenstein index is not divisible by $p$. Furthermore, we also show that the $F$-jumping numbers of ${\tau }_b(R;\Delta ,a^t)$ are discrete under the more general assumption that $K_R+\Delta$ is $\bR$-Cartier.

7 pages, minor changes, to appear in Proceedings of the American Mathematical Society

References in corpus (3)

• F-thresholds and Bernstein-Sato polynomials
• Test ideals via algebras of $p^{-e}$-linear maps
• Test ideals in non-Q-Gorenstein rings

Cited by in corpus (2)

• A survey of test ideals
• Castelnuovo-Mumford regularity and the discreteness of $F$-jumping coefficients in graded rings