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The support of top graded local cohomology modules

Katzman, M. (2003) The support of top graded local cohomology modules. arXiv:math/0312333v1 [math.AC]. (Unpublished)

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Abstract

Let $R_0$ be any domain, let $R=R_0[U_1, ..., U_s]/I$, where $U_1, ..., U_s$ are indeterminates of some positive degrees, and $I\subset R_0[U_1, ..., U_s]$ is a homogeneous ideal. The main theorem in this paper is states that all the associated primes of $H:=H^s_{R_+}(R)$ contain a certain non-zero ideal $c(I)$ of $R_0$ called the ``content'' of $I$. It follows that the support of $H$ is simply $V(\content(I)R + R_+)$ (Corollary 1.8) and, in particular, $H$ vanishes if and only if $c(I)$ is the unit ideal. These results raise the question of whether local cohomology modules have finitely many minimal associated primes-- this paper provides further evidence in favour of such a result. Finally, we give a very short proof of a weak version of the monomial conjecture based on these results.

Item Type: Article
Copyright, Publisher and Additional Information: © 2003 Katzman. Imported from arXiv
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Miss Anthea Tucker
Date Deposited: 20 Nov 2009 10:50
Last Modified: 08 Feb 2013 16:59
Status: Unpublished
Related URLs:
URI: http://eprints.whiterose.ac.uk/id/eprint/10161

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