Tate (co)homology via pinched complexes

Lars Winther Christensen, David A. Jorgensen

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

For complexes of modules we study two new constructions which we call the pinched tensor product and the pinched Hom. They provide new methods for computing Tate homology Tor and Tate cohomology Ext, which lead to conceptual proofs of balancedness of Tate (co)homology for modules over associative rings. Another application we consider is in local algebra. Under conditions of the vanishing of Tate (co)homology, the pinched tensor product of two minimal complete resolutions yields a minimal complete resolution.

Original languageEnglish
Pages (from-to)667-689
Number of pages23
JournalTransactions of the American Mathematical Society
Volume366
Issue number2
DOIs
StatePublished - 2014

Keywords

  • Balancedness
  • Tate cohomology
  • Tate homology
  • Total acyclicity

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