Symmetry in vanishing of Tate cohomology over Gorenstein rings

Abstract

We investigate symmetry in the vanishing of Tate cohomology for finitely generated modules over local Gorenstein rings. For finitely generated R-modules M and N over Gorenstein local ring R, it is shown that ${\widehat{Ext}}_R^i(M,N)=0$ for all $i\in \mathbb{Z}$ if and only if ${\widehat{Ext}}_R^i(N,M)=0$ for all $i\in \mathbb{Z}$.

Revised version, Lemma 3.3 has been added

References in corpus (1)

• Auslander-Reiten conjecture and Auslander-Reiten duality