Bass numbers of semigroup-graded local cohomology


Journal Article

Given a module M over a ring R that has a grading by a semigroup Q, we present a spectral sequence that computes the local cohomology HIi(M) at any graded ideal I in terms of Ext modules. We use this method to obtain flniteness results for the local cohomology of graded modules over semigroup rings. In particular we prove that for a semigroup Q whose saturation Qsat is simplicial, and a finitely generated module M over k[Q] that is graded by Qgp, the Bass numbers of HIi(M) are finite for any Q-graded ideal I of k[Q]. Conversely, if Qsat is not simplicial, we find a graded ideal I and graded k[Q]-module M such that the local cohomology module HIi(M) has infinite-dimensional socle. We introduce and exploit the combinatorially defined essential set of a semigroup.

Full Text

Duke Authors

Cited Authors

  • Helm, D; Miller, E

Published Date

  • January 1, 2003

Published In

Volume / Issue

  • 209 / 1

Start / End Page

  • 41 - 66

International Standard Serial Number (ISSN)

  • 0030-8730

Digital Object Identifier (DOI)

  • 10.2140/pjm.2003.209.41

Citation Source

  • Scopus