A note on discreteness of 𝐹-jumping numbers

Schwede, Karl

doi:10.1090/S0002-9939-2011-10825-6

A note on discreteness of $F$-jumping numbers
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Proc. Amer. Math. Soc. 139 (2011), 3895-3901 Request permission

Abstract:

Suppose that $R$ is a ring essentially of finite type over a perfect field of characteristic $p > 0$ and that $\mathfrak {a} \subseteq R$ is an ideal. We prove that the set of $F$-jumping numbers of $\tau _b(R; \mathfrak {a}^t)$ has no limit points under the assumption that $R$ is normal and $\mathbb {Q}$-Gorenstein – we make no assumption as to whether the $\mathbb {Q}$-Gorenstein index is divisible by $p$. Furthermore, we also show that the $F$-jumping numbers of $\tau _b(R; \Delta , \mathfrak {a}^t)$ are discrete under the more general assumption that $K_R + \Delta$ is $\mathbb {R}$-Cartier.

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