  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.
