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

详细信息    查看全文

• 作者：Yan Ping Liu ; Zhong Kui Liu ; Xiao Yan Yang
• 刊名：Acta Mathematica Sinica
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：32
• 期：7
• 页码：831-844
• 全文大小：242 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Chinese Library of Science
  
• 出版者：Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society, co-published
• ISSN：1439-7617
• 卷排序：32

文摘

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.KeywordsTate homologystable homologycomplete projective resolution