English

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.

Keywords

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

R2 v1 2026-07-22T16:47:41.078Z