Finiteness properties of local cohomology modules: A characteristic-free approach

DOI10.1016/S0022-4049(99)00080-8zbMath0964.13010MaRDI QIDQ1577498

Gennady Lyubeznik

Publication date: 16 July 2001

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

zbMATH Keywords

associated primesBass numbers\(D\)-modules

Mathematics Subject Classification ID

Commutative Noetherian rings and modules (13E05) Local cohomology and commutative rings (13D45) Commutative rings and modules of finite generation or presentation; number of generators (13E15) Modules of differentials (13N05)

Related Items (17)

The $D$–module structure of $R[F$–modules] ⋮ Lyubeznik Table of Sequentially Cohen–Macaulay Rings ⋮ Local Cohomology—An Invitation ⋮ Some results on local cohomology of polynomial and formal power series rings: the one dimensional case ⋮ Generalized Lyubeznik numbers ⋮ \(D\)-modules, Bernstein-Sato polynomials and \(F\)-invariants of direct summands ⋮ Associated primes of local cohomology of flat extensions with regular fibers and \(\varSigma\)-finite \(D\)-modules ⋮ Socle finiteness of the local cohomology ⋮ Coassociated primes of local homology and local cohomology modules ⋮ A dichotomy for the injective dimension ofF-finiteF-modules and holonomicD-modules ⋮ $D$-module structure of local cohomology modules of toric algebras ⋮ Annihilators of local cohomology modules and simplicity of rings of differential operators ⋮ A characteristic-free proof of a basic result on \(\mathcal D\)-modules ⋮ Local cohomology modules of polynomial or power series rings over rings of small dimension ⋮ On finiteness properties of local cohomology modules over Cohen-Macaulay local rings ⋮ Comparison of local cohomlogy modules of a ring and its amalgamated algebra along a given ideal ⋮ Properties of Lyubeznik numbers under localization and polarization

Cites Work

• Unnamed Item
• Finiteness properties of local cohomology modules (an application of \(D\)- modules to commutative algebra)
• Injective dimension of \(D\)-modules: A characteristic-free approach
• Éléments de géométrie algébrique. IV: Étude locale des schémas et des morphismes de schémas (Quatrième partie). Rédigé avec la colloboration de J. Dieudonné
• On the ubiquity of Gorenstein rings
• Bass Numbers of Local Cohomology Modules
• F-modules: applications to local cohomology and D-modules in characteristic p>0.

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