Algorithms for graded injective resolutions and local cohomology over semigroup rings

• Autores: Ezra Miller, David Helm
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 39, Nº 3, 2005, págs. 373-395
• Idioma: inglés
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• Resumen

  • Let Q be an affine semigroup generating , and fix a finitely generated -graded module M over the semigroup algebra for a field . We provide an algorithm to compute a minimal -graded injective resolution of M up to any desired cohomological degree. As an application, we derive an algorithm computing the local cohomology modules supported on any monomial (that is, -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.