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TitleAlgorithms for graded injective resolutions and local cohomology over semigroup rings
Author(s) David Helm, Ezra Miller
TypeArticle in Journal
AbstractLet 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.
KeywordsSemigroup ring, Local cohomology, Graded-injective resolution, Computation, Gröbner basis, Sector partition, Irreducible hull, Monomial matrix, Convex polyhedron, Lattice point
URL http://www.sciencedirect.com/science/article/pii/S074771710500009X
JournalJournal of Symbolic Computation
Pages373 - 395
NoteSpecial issue on the occasion of MEGA 2003 MEGA 2003
Translation No
Refereed No