Vanishing of Tate homology - An application of stable homology for complexes

Authors
Liu, Yan Ping Liu, Zhong Kui Yang, Xiao Yan
Citation
Liu, Yan Ping et al., Vanishing of Tate homology - An application of stable homology for complexes, Acta mathematica Sinica. English series (Print) , 32(7), 2016, pp. 831-844
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
32
Issue
7
Year of publication
2016
Pages
831 - 844
Database
ACNP
SICI code
Abstract
It has been proved that the vanishing of Tate homology is a sufficient condition for the derived depth formula to hold in [J. Pure Appl. Algebra, 219, 464.481 (2015)]. In this paper, we investigate when Tate homology vanishes by studying the stable homology theory for complexes. Properties such as the balancedness and vanishing of stable homology for complexes are studied. Our results show that the vanishing of this homology can detect finiteness of homological dimensions of complexes and regularness of rings.