TY - JOUR
T1 - Vanishing of Tate homology and depth formulas over local rings
AU - Christensen, Lars Winther
AU - Jorgensen, David A.
N1 - Publisher Copyright:
© 2014 Elsevier B.V.
PY - 2015/3/1
Y1 - 2015/3/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84918825129&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2014.05.005
DO - 10.1016/j.jpaa.2014.05.005
M3 - Article
AN - SCOPUS:84918825129
SN - 0022-4049
VL - 219
SP - 464
EP - 481
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 3
ER -