  Auslander's depth formula for pairs of Tor-independent modules over a regular
local ring, depth(M \otimes 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.
