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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Tate (co)homology via pinched complexes


Authors: Lars Winther Christensen and David A. Jorgensen
Journal: Trans. Amer. Math. Soc. 366 (2014), 667-689
MSC (2010): Primary 16E05, 16E30; Secondary 13D07, 18G25
Published electronically: May 16, 2013
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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.


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Additional Information

Lars Winther Christensen
Affiliation: Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409
Email: lars.w.christensen@ttu.edu

David A. Jorgensen
Affiliation: Department of Mathematics, University of Texas, Arlington, Texas 76019
Email: djorgens@uta.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05746-7
PII: S 0002-9947(2013)05746-7
Keywords: Balancedness, Tate cohomology, Tate homology, total acyclicity
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.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.