Vanishing of Tate homology and depth formulas over local rings

Auslander's depth formula for pairs of Tor-independent modules over a regular local ring, depth(M⊗RN)=depthM+depthN−depthR, has been generalized in several directions; most significantly it has been shown to hold for pairs of Tor-independent modules over complete intersection rings.In this paper we establish a depth formula that holds for every pair of Tate Tor-independent modules over a Gorenstein local ring. It subsumes previous generalizations of Auslander's formula and yields new results on vanishing of cohomology over certain Gorenstein rings.