Twenty-Four Hours of Local Cohomology

2007/11/06 by Srikanth B. Iyengar, Graham Leuschke, Anton Leykin +4 · 158 citations
Mathematics · #Commutative Algebra and Its Applications #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Mathematics

paper · doi:10.1090/gsm/087

published in Graduate studies in mathematics (American Mathematical Society)

openalex publication_date 2007/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

Basic notions Cohomology Resolutions and derived functors Limits Gradings, filtrations, and Grobner bases Complexes from a sequence of ring elements Local cohomology Auslander-Buchsbaum formula and global dimension Depth and cohomological dimension Cohen-Macaulay rings Gorenstein rings Connections with sheaf cohomology Projective varieties The Hartshorne-Lichtenbaum vanishing theorem Connectedness Polyhedral applications D-modules Local duality revisited De Rham cohomology Local cohomology over semigroup rings The Frobenius endomorphism Curious examples Algorithmic aspects of local cohomology Holonomic rank and hypergeometric systems Injective moduels and Matlis duality Bibliography Index.

Cited by

• Alexander modules, Mellin transformation and variations of mixed Hodge structures
• (Non)Vanishing results on local cohomology of valuation rings
• Cohomology Vanishing theorems over some rings containing nilpotents
• Local cohomology [wikipedia]

Related

• Local cohomology -- an invitation
• Graded local cohomology of modules over semigroup rings
• Notes on endomorphisms, local cohomology and completion
• Generalized local duality, canonical modules, and prescribed bound on projective dimension
• Local Cohomology and complete intersections of rank 1