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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Cyclic covers of rings with rational singularities


Author: Anurag K. Singh
Journal: Trans. Amer. Math. Soc. 355 (2003), 1009-1024
MSC (2000): Primary 13A35, 13A02; Secondary 13H10, 14B05
Published electronically: November 1, 2002
MathSciNet review: 1938743
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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

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03186-0
PII: S 0002-9947(02)03186-0
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
Article copyright: © Copyright 2002 American Mathematical Society