A note on discreteness of $F$-jumping numbers

Details A note on discreteness of $F$-jumping numbers A note on discreteness of $F$-jumping numbers

2010-04-08

arxiv.org/abs/1004.1377v2

Proc. Amer. Math. Soc. 139 (2011), no. 11, 3895-3901

Mathematics

Commutative Algebra

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

Scientific paper

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.

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