Vanishing of Tate homology and depth formulas over local rings

2011/07/15 by Lars Winther Christensen, Christensen, Lars Winther, David A. Jorgensen +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Primary 13D07. Secondary 13D02

paper · pdf · doi:10.48550/arxiv.1107.3102

openalex publication_date 2011/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Acyclicity versus total acyclicity for complexes over noetherian rings

Related

• Vanishing of relative homology and depth of tensor products
• On Auslander`s depth formula
• A note on the depth formula and vanishing of cohomology
• A study of Tate homology via the approximation theory with applications to the depth formula
• On the depth of tensor products of modules