Algorithms for graded injective resolutions and local cohomology over semigroup rings

Details Algorithms for graded injective resolutions and local cohomology over semigroup rings Algorithms for graded injective resolutions and local cohomology over semigroup rings

2003-09-16

arxiv.org/abs/math/0309256v1

Mathematics

Commutative Algebra

22 pages, no figures

Scientific paper

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.

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