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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
DOI: https://doi.org/10.1090/S0002-9939-2011-10825-6
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
MR Author ID: 773868
Email: schwede@math.psu.edu

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.