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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Cyclic covers of rings with rational singularities
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by Anurag K. Singh PDF
Trans. Amer. Math. Soc. 355 (2003), 1009-1024 Request permission

Abstract:

We examine some recent work of Phillip Griffith on étale covers and fibered products from the point of view of tight closure theory. While it is known that cyclic covers of Gorenstein rings with rational singularities are Cohen-Macaulay, we show this is not true in general in the absence of the Gorenstein hypothesis. Specifically, we show that the canonical cover of a $\mathbb Q$-Gorenstein ring with rational singularities need not be Cohen-Macaulay.
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Additional Information
  • Anurag K. Singh
  • Affiliation: Department of Mathematics, University of Utah, 155 S. 1400 E., Salt Lake City, Utah 84112-0090
  • Address at time of publication: Mathematical Sciences Research Institute, 1000 Centennial Drive, #5070, Berkeley, California 94720-5070
  • Email: asingh@msri.org
  • Received by editor(s): August 21, 2002
  • Published electronically: November 1, 2002
  • Additional Notes: This manuscript is based on work supported in part by the National Science Foundation under Grant No. DMS 0070268. I would like to thank the referee for a careful reading of the manuscript and for helpful suggestions.

  • Dedicated: Dedicated to Professor Phillip Griffith on the occasion of his sixtieth birthday
  • © Copyright 2002 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 355 (2003), 1009-1024
  • MSC (2000): Primary 13A35, 13A02; Secondary 13H10, 14B05
  • DOI: https://doi.org/10.1090/S0002-9947-02-03186-0
  • MathSciNet review: 1938743