A unified approach to formal local cohomology and local Tate cohomology

Abstract

Let $R$ be a commutative Noetherian ring. We introduce a theory of formal local cohomology for complexes of $R$-modules. As an application, we establish some relations between formal local cohomology, local homology, local cohomology and local Tate cohomology through some natural isomorphisms. We investigate vanishing of formal local cohomology modules. Also, we give a characterization of Cohen-Macaulay complexes.