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Local cohomology modules with infinite dimensional socles


Authors: Thomas Marley and Janet C. Vassilev
Journal: Proc. Amer. Math. Soc. 132 (2004), 3485-3490
MSC (2000): Primary 13D45
DOI: https://doi.org/10.1090/S0002-9939-04-07658-0
Published electronically: July 22, 2004
MathSciNet review: 2084068
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Abstract: In this paper we prove the following generalization of a result of Hartshorne: Let $T$ be a commutative Noetherian local ring of dimension at least two, $R=T[x_1,\dots,x_n]$, and $I=(x_1,\ldots,x_n)$. Let $f$ be a homogeneous element of $R$ such that the coefficients of $f$ form a system of parameters for $T$. Then the socle of $H^n_I(R/fR)$ is infinite dimensional.


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Additional Information

Thomas Marley
Affiliation: Department of Mathematics, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0323
Email: tmarley@math.unl.edu

Janet C. Vassilev
Affiliation: Department of Mathematical Sciences, University of Arkansas, Fayetteville, Arkan- sas 72701
Email: jvassil@uark.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07658-0
Keywords: Local cohomology
Received by editor(s): July 16, 2003
Published electronically: July 22, 2004
Additional Notes: The first author was partially supported by NSF grant DMS-0071008.
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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