Vanishing of Tate homology and depth formulas over local rings

By L. Christensen, David A. Jorgensen. 2011

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/273f49ed21a0df55f0d6bdfe257396d736dd5261