The cohomology algebra of a commutative group scheme

Commutative Algebra in Group Cohomology . 3

We apply constructions from equivariant topology to Benson-Carlson resolutions and hence prove in (2.1) that the group cohomology ring of a nite 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 cohom...

Tate Cohomology in Commutative Algebra.

Commutative Algebra Commutative Algebra : General

The First Cohomology Group of the Generalized Morava Stabilizer Algebra

There exists a p-local spectrum T (m) with BP∗(T (m))= BP∗[t1, . . . , tm]. Its Adams-Novikov E2-term is isomorphic to ExtΓ(m+1)(BP∗, BP∗), where Γ(m+ 1) = BP∗(BP )/ (t1, . . . , tm) = BP∗[tm+1, tm+2, . . . ]. In this paper we determine the groups ExtΓ(m+1)(BP∗, v −1 n BP∗/In) for all m,n > 0. Its rank ranges from n + 1 to n2 depending on the value of m.

Modules and Cohomology over Group Algebras. One Commutative Algebraist’s Perspective

In this article I have attempted to explain basic constructions and results on group algebras and their cohomology. My aim is to provide the background necessary for a novice in this subject to begin reading Dave Benson’s article in these proceedings. The presentation is not always systematic, and is probably idiosyncratic. The available accounts of the subject, be they Benson’s own books [7], ...