Tate cohomology in commutative algebra

Tate Cohomology in Commutative Algebra.

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...

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...

Finite Generation of Tate Cohomology

Let G be a finite group and let k be a field of characteristic p. Given a finitely generated indecomposable non-projective kG-module M , we conjecture that if the Tate cohomology Ĥ ∗ (G, M) of G with coefficients in M is finitely generated over the Tate cohomology ring Ĥ ∗ (G, k), then the support variety VG(M) of M is equal to the entire maximal ideal spectrum VG(k). We prove various results w...