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arXiv · 1107.3102

Vanishing of Tate homology and depth formulas over local rings

Lars Winther Christensen·David A. Jorgensen
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Abstract

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.

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Lars Winther Christensen, David A. Jorgensen. 2011-07-15. Vanishing of Tate homology and depth formulas over local rings. https://arxiv.org/abs/1107.3102

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