Commutative algebra in group cohomology Original Research Article

We apply constructions from equivariant topology to Benson-Carlson resolutions and hence prove in (2.1) that the group cohomology ring of a finite group enjoys remarkable duality properties based on its global geometry. This recovers and generalizes the result of Benson-Carlson stating that a Cohen-Macaulay cohomology ring is automatically Gorenstein. We give an alternative approach to Tate cohomology of groups and in (4.1) show that the Tate cohomology of a group is close to being the cohomology of the projective space of the group cohomology ring.