Algorithms for graded injective resolutions and local cohomology over semigroup rings
Commutative Algebra
2007-05-23 v1
Abstract
Let Q be an affine semigroup generating Z^d, and fix a finitely generated Z^d-graded module M over the semigroup algebra k[Q] for a field k. We provide an algorithm to compute a minimal Z^d-graded injective resolution of M up to any desired cohomological degree. As an application, we derive an algorithm computing the local cohomology modules H^i_I(M) supported on any monomial (that is, Z^d-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.
Keywords
Cite
@article{arxiv.math/0309256,
title = {Algorithms for graded injective resolutions and local cohomology over semigroup rings},
author = {David Helm and Ezra Miller},
journal= {arXiv preprint arXiv:math/0309256},
year = {2007}
}
Comments
22 pages, no figures