Details:
Title  Algorithms for graded injective resolutions and local cohomology over semigroup rings  Author(s)  David Helm, Ezra Miller  Type  Article in Journal  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  Semigroup ring, Local cohomology, Gradedinjective resolution, Computation, Gröbner basis, Sector partition, Irreducible hull, Monomial matrix, Convex polyhedron, Lattice point  ISSN  07477171 
URL 
http://www.sciencedirect.com/science/article/pii/S074771710500009X 
Language  English  Journal  Journal of Symbolic Computation  Volume  39  Number  3–4  Pages  373  395  Year  2005  Note  Special issue on the occasion of MEGA 2003 MEGA 2003  Edition  0  Translation 
No  Refereed 
No 
