Tate Cohomology over Fairly General Rings
نویسنده
چکیده
Tate cohomology was originally defined over finite groups. More recently, Avramov and Martsinkovsky showed how to extend the definition so that it now works well over Gorenstein rings. This paper improves the theory further by giving a new definition that works over more general rings, specifically, those with a dualizing complex. The new definition of Tate cohomology retains the desirable properties established by Avramov and Martsinkovsky. Notably, there is a long exact sequence connecting it to ordinary Ext groups. 0. Introduction Tate cohomology was originally defined over finite groups, and has been used to great effect in group representation theory. More recently, Avramov and Martsinkovsky accomplished in [1] an extension of the definition so that it now works well over Gorenstein rings. In fact, [1] went so far as to define Tate Ext groups,
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