We show that for a discrete group G, the equivariant cohomology of a G-space X with G-local coefficients M is isomorphic to the Bredon-Iliman cohomology of X with equivariant local coefficients M.

The natural transformation Ξ from L–theory to the Tate cohomology of Z/2 acting on K–theory (constructed in [WW2] and [WW3]) commutes with external products. Corollary: The Tate cohomology of Z/2 acting on the K–theory of any ring with involution is a generalized Eilenberg–MacLane spectrum, and it is 4–periodic.

In this paper we study the local cohomology of all finitely generated bigraded modules over a standard bigraded polynomial ring which have only one nonvanishing local cohomology with respect to one of the irrelevant bigraded ideals.

Using local cohomology and algebraic D-Modules, we generalize a comparison theorem between relative de Rham cohomology and Dwork cohomology due to N. Katz, A. Adolphson and S. Sperber.