Local cohomology modules with infinite dimensional socles
Commutative Algebra
2007-05-23 v1
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.
Cite
@article{arxiv.math/0209196,
title = {Local cohomology modules with infinite dimensional socles},
author = {Thomas Marley and Janet C. Vassilev},
journal= {arXiv preprint arXiv:math/0209196},
year = {2007}
}
Comments
6 pages