Commutative algebra in group cohomology

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

Local Cohomology in Commutative

The notion of local cohomology was prominent in the summer school; in this volume it puts in explicit appearances in the papers of Greenlees and Huneke/Taylor, and figures at least peripherally in material related to the paper of Adem. The aim of this short account is to introduce local cohomology and, in a very sketchy way, tie together some of its various manifestations. There are some real d...

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], ...