Local cohomology modules with infinite dimensional socles

Marley, Thomas; Vassilev, Janet

doi:10.1090/S0002-9939-04-07658-0

Local cohomology modules with infinite dimensional socles
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by Thomas Marley and Janet C. Vassilev

Proc. Amer. Math. Soc. 132 (2004), 3485-3490

DOI: https://doi.org/10.1090/S0002-9939-04-07658-0

Published electronically: July 22, 2004

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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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