Local cohomology modules and Cousin complexes

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 Hsa(Ht−1(CR(F,X))) and Hs′−1(Ht′a(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.