Tate cohomology in commutative algebra

Abstract

We construct local Tate cohomology groups H ̂ ∗ I (A;M) of an A-module M at a finitely generated ideal I by splicing together the Grothendieck local cohomology groups [16] with the local homology groups of [14]. We give two quite different means of calculating them, show they vanish on I-free modules and prove that many elements of A act invertibly. These local Tate groups have applications in the study of completion theorems and their duals in equivariant topology.