On local cohomology modules
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 \(H^{n}_{I}(A)=0\).
Matlis dual of the local cohomology module
scientific article; zbMATH DE number 3973012
scientific article