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

DOI:
https://doi.org/10.1090/S0002-9947-02-03186-0

Published electronically:
November 1, 2002

MathSciNet review:
1938743

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Abstract | References | Similar Articles | Additional Information

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 -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:
https://doi.org/10.1090/S0002-9947-02-03186-0

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