2000/10/01 by David Helm, Ezra Miller, Helm, David +1
Computer Science · Mathematics · #05E99 #13D45 (Primary) #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis #math.AC #math.AG #math.CO #msc:05E99 #msc:13D45
paper · pdf · doi:10.48550/arxiv.math/0010003
19 pages LaTeX, 1 figure (.eps) Definition 5.1 corrected; transcription error in Theorem 7.1.3 fixed
openalex publication_date 2000/10/01 · arxiv created 2000/10/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a module M over a ring R which has a grading by a semigroup Q, we present a spectral sequence that computes the local cohomology of M at any Q-graded ideal I in terms of Ext modules. This method is used to obtain finiteness results for the local cohomology of graded modules over semigroup rings; in particular we prove that for a semigroup Q whose saturation is simplicial, the Bass numbers of such local cohomology modules are finite. Conversely, if the saturation of Q is not simplicial, one can find a graded ideal I and a graded R-module M whose local cohomology at I in some degree has an infinite-dimensional socle. We introduce and exploit the combinatorially defined essential set of a semigroup.