Vanishing of Tate homology and depth formulas over local rings

• Lars Winther Christensen ^[1] ; David A. Jorgensen ^[2]
  1. [1] Texas Tech University

     Texas Tech University

     Estados Unidos

     
  2. [2] University of Texas (USA)
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 3 ((March 2015)), 2015 (Ejemplar dedicado a: Special Issue in honor of Prof. Hans-Bjørn Foxby), págs. 464-481
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.05.005
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• Resumen

  • 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.