Extension Functors of Cousin Cohomology Modules

Let R be a commutative Noetherian ring with non-zero identity, a filtration of Spec(R) which admits an R-module X, and C-R (T, X) the Cousin complex for X with respect to T. In this paper, we first introduce the Cousin functor and the Cousin spectral sequences. Then for non-negative integers s, t and a finite R-module N, we study the membership of R-modules Hs-1 (Ext(R)(t )(N, C-R (F, X))) and Ext(R)(t ) (N, H-t(-1) (C-R(F, X))) in Serre subcategories of the category of R-modules and find some conditions for validity of an isomorphism between them. Finally, we use these results to present some facts about the vanishing and finiteness of Cousin cohomology modules.