Algorithms for graded injective resolutions and local cohomology over semigroup rings


Journal Article

Let Q be an affine semigroup generating ℤd, and fix a finitely generated ℤd-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal ℤd-graded injective resolution of M up to any desired cohomological degree. As an application, we derive an algorithm computing the local cohomology modules HIi supported on any monomial (that is, ℤd-graded) ideal I. Since these local cohomology modules are neither finitely generated nor finitely cogenerated, part of this task is defining a finite data structure to encode them. © 2005 Elsevier Ltd. All rights reserved.

Full Text

Duke Authors

Cited Authors

  • Helm, D; Miller, E

Published Date

  • March 1, 2005

Published In

Volume / Issue

  • 39 / 3-4 SPEC. ISS.

Start / End Page

  • 373 - 395

International Standard Serial Number (ISSN)

  • 0747-7171

Digital Object Identifier (DOI)

  • 10.1016/j.jsc.2004.11.009

Citation Source

  • Scopus