An example of an infinite set of associated primes of a local cohomology module

Katzman, M. (2002) An example of an infinite set of associated primes of a local cohomology module. Journal of Algebra, 252 (1). pp. 161-166. ISSN 0021-8693

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Abstract

Let $(R,m)$ be a local Noetherian ring, let $I\subset R$ be any ideal and let $M$ be a finitely generated $R$-module. In 1990 Craig Huneke conjectured that the local cohomology modules $H^i_I(M)$ have finitely many associated primes for all $i$. In this paper I settle this conjecture by constructing a local cohomology module of a local $k$-algebra with an infinite set of associated primes, and I do this for any field $k$.

Item Type:	Article
Copyright, Publisher and Additional Information:	© 2002 Elsevier. This is an author produced version of a paper subsequently published in Journal of Algebra. Uploaded in accordance with the publisher's self-archiving policy.
Keywords:	graded commutative Noetherian ring; graded local cohomology module; infinite set of associated primes
Academic Units:	The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User:	Miss Anthea Tucker
Date Deposited:	19 Nov 2009 15:54
Last Modified:	08 Feb 2013 16:59
Published Version:	http://dx.doi.org/doi:10.1016/S0021-8693(02)00032-...
Status:	Published
Publisher:	Elsevier
Identification Number:	10.1016/S0021-8693(02)00032-7
URI:	http://eprints.whiterose.ac.uk/id/eprint/10159

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