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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on discreteness of $F$-jumping numbers
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by Karl Schwede PDF
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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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
  • 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
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2823035