On local cohomology modules
type: Item
instance of: scholarly article
title: On local cohomology modules
zbMATH Open document ID: 0603.13012
DOI: 10.1016/0022-4049(86)90089-7
author: Frederick W. Call
published in: Journal of Pure and Applied Algebra
publication date: 1986-01-01T00:00:00Z
review text: Let I be an ideal in an n-dimensional local ring (A,m). The Matlis dual of the local cohomology module \(H^{n}_{I}(A)^*\) is shown to be equal to a dual of a torsion submodule of the canonical module of \(\hat A\) (the completion of A). This generalizes results by R. Y. Sharp and J. Herzog - E. Kunz. It also gives as a corollary a theorem by R. Hartshorne characterizing the vanishing of \(H^{n}_{I}(A)\) in terms of Spec A. In the second section of the article the associated primes to \(H_{I}^{n- 1}(A)^*\) of height \(>0\) are characterized provided A is Gorenstein and \(H^{n}_{I}(A)=0\).
Mathematics Subject Classification ID: 13D03
Mathematics Subject Classification ID: 14B15
zbMATH DE Number: 3973012
zbMATH Keywords: local ring
zbMATH Keywords: Matlis dual of the local cohomology module
MaRDI profile type: Publication
full work available at URL: 0022-4049(86)90089-7
OpenAlex ID: W2057767372
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description: scientific article; zbMATH DE number 3973012