Local cohomology modules and Cousin complexes

Document Type : Research Paper

Authors

Department of Mathematics, Payame Noor University (PNU), P.O.BOX, 19395-4697, Tehran, Iran

Abstract

Let R be a commutative Noetherian ring with non-zero identity, a an ideal of R, X an arbitrary R--module, F a filtration of Spec(R) which admits X, and s,s,t,t non-negative integers such that s+t=s+t. In this paper, we study the membership of R--modules Has(Ht1(CR(F,X))) and Hs1(Hat(CR(F,X))) in Serre subcategories of the category of R--modules and find some sufficient conditions which ensure the existence of an isomorphism between them, where CR(F,X) is the Cousin complex for X with respect to F. As applications, we give some new facts and represent some older facts about the local cohomology modules and the Cousin complexes.

Keywords


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