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Local cohomology modules with infinite dimensional socles

Thomas Marley·Janet C. Vassilev
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Abstract

Let T be a commutative Noetherian local ring of dimension at least two and R=T[x_1,...,x_n] a polynomial ring in n variables over T. Consider R as a graded ring with deg T = 0 and deg x_i = 1 for all i. Let I=R_+ and f a homogeneous polynomial whose coefficients form a system of parameters for T. We show that the socle of H^n_I(R/fR) is infinite dimensional, generalizing an example due to Hartshorne.

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Thomas Marley, Janet C. Vassilev. 2002-09-16. Local cohomology modules with infinite dimensional socles. https://arxiv.org/abs/math/0209196

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