Local cohomology modules with infinite dimensional socles
Abstract
Let T be a commutative Noetherian local ring of dimension at least two and R=T[x1,...,xn] a polynomial ring in n variables over T. Consider R as a graded ring with deg T = 0 and deg xi = 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 HnI(R/fR) is infinite dimensional, generalizing an example due to Hartshorne.
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