Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



A note on discreteness of $ F$-jumping numbers

Author: Karl Schwede
Journal: Proc. Amer. Math. Soc. 139 (2011), 3895-3901
MSC (2000): Primary 13A35, 14F18, 14B05
Published electronically: June 28, 2011
MathSciNet review: 2823035
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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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Additional Information

Karl Schwede
Affiliation: Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802

Keywords: Test ideal, jumping number, $\mathbb{Q}$-Gorenstein, multiplier ideal
Received by editor(s): April 8, 2010
Received by editor(s) in revised form: October 4, 2010
Published electronically: June 28, 2011
Additional Notes: The author was partially supported by a National Science Foundation postdoctoral fellowship and by NSF grant DMS-1064485/0969145.
Communicated by: Irena Peeva
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.