Tate (co)homology via pinched complexes
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- by Lars Winther Christensen and David A. Jorgensen PDF
- Trans. Amer. Math. Soc. 366 (2014), 667-689 Request permission
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 $\operatorname {\widehat {Tor}}$ and Tate cohomology $\operatorname {\widehat {Ext}}$, 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.References
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Additional Information
- Lars Winther Christensen
- Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
- MR Author ID: 671759
- ORCID: 0000-0002-9360-123X
- Email: lars.w.christensen@ttu.edu
- David A. Jorgensen
- Affiliation: Department of Mathematics, University of Texas, Arlington, Texas 76019
- Email: djorgens@uta.edu
- Received by editor(s): May 12, 2011
- Received by editor(s) in revised form: November 9, 2011, and November 13, 2011
- Published electronically: May 16, 2013
- Additional Notes: The first author was partially supported by NSA grant H98230-11-0214.
The second author was partially supported by NSA grant H98230-10-0197. - © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 667-689
- MSC (2010): Primary 16E05, 16E30; Secondary 13D07, 18G25
- DOI: https://doi.org/10.1090/S0002-9947-2013-05746-7
- MathSciNet review: 3130313