Vanishing of Tate homology and depth formulas over local rings
Abstract
Auslander's depth formula for pairs of Tor-independent modules over a regular local ring, depth(M N) = depth(M) + depth(N) - depth(R), has been generalized in several directions over a span of four decades. 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 eneralizations of Auslander's formula and yields exact bounds for vanishing of cohomology over certain Gorenstein rings.
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