A unified approach to formal local cohomology and local Tate cohomology
  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. 
Mohsen Asgharzadeh and Kamran Divaani-Aazar
math.AC