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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the existence of maximal Cohen-Macaulay modules over $p\,\text{th}$ root extensions


Author: Daniel Katz
Journal: Proc. Amer. Math. Soc. 127 (1999), 2601-2609
MSC (1991): Primary 13B21, 13B22, 13H05, 13H15
Published electronically: April 15, 1999
MathSciNet review: 1605976
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Abstract: Let $S$ be an unramified regular local ring having mixed characteristic $p > 0$ and $R$ the integral closure of $S$ in a $p$th root extension of its quotient field. We show that $R$ admits a finite, birational module $M$ such that $depth(M) = dim(R)$. In other words, $R$ admits a maximal Cohen-Macaulay module.


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Additional Information

Daniel Katz
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: dlk@math.ukans.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04880-7
PII: S 0002-9939(99)04880-7
Received by editor(s): August 26, 1997
Received by editor(s) in revised form: November 26, 1997
Published electronically: April 15, 1999
Communicated by: Wolmer V. Vasconcelos
Article copyright: © Copyright 1999 American Mathematical Society