Bass Numbers of Semigroup-Graded Local Cohomology
Abstract
Given a module M over a ring R which has a grading by a semigroup Q, we present a spectral sequence that computes the local cohomology of M at any Q-graded ideal I in terms of Ext modules. This method is used to obtain finiteness results for the local cohomology of graded modules over semigroup rings; in particular we prove that for a semigroup Q whose saturation is simplicial, the Bass numbers of such local cohomology modules are finite. Conversely, if the saturation of Q is not simplicial, one can find a graded ideal I and a graded R-module M whose local cohomology at I in some degree has an infinite-dimensional socle. We introduce and exploit the combinatorially defined essential set of a semigroup.
Keywords
Cite
@article{arxiv.math/0010003,
title = {Bass Numbers of Semigroup-Graded Local Cohomology},
author = {David Helm and Ezra Miller},
journal= {arXiv preprint arXiv:math/0010003},
year = {2007}
}
Comments
19 pages LaTeX, 1 figure (.eps) Definition 5.1 corrected; transcription error in Theorem 7.1.3 fixed