Algorithms for graded injective resolutions and local cohomology over semigroup rings
David Helm, Ezra Miller
Abstract
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(M) 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.
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