Tate cohomology

General Introduction
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Search results
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Online References
Greenlees: Tate cohomology in commutative algebra
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Paper References
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Definition
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Properties
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Standard theorems
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Open Problems
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Connections to Number Theory
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Computations and Examples
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History and Applications
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Some Research Articles
Something on Freyd's generating hypothesis: K0814
Greenlees: Tate cohomology in axiomatic stable homotopy theory
arXiv:1209.4888 Tate and TateHochschild Cohomology for finite dimensional Hopf Algebras from arXiv Front: math.KT by Van C. Nguyen Let A be any finite dimensional Hopf algebra over a field k. We generalize the notion of Tate cohomology for A, which is defined in both positive and negative degrees, and compare it with the TateHochschild cohomology of A that was presented by Bergh and Jorgensen. We introduce cup products that make the Tate and TateHochschild cohomology of A become graded rings. We establish the relationship between these rings, which turns out to be similar to that in the ordinary nonTate cohomology case. As an example, we explicitly compute the TateHochschild cohomology for a finite dimensional (cyclic) group algebra. In another example, we compute both the Tate and TateHochschild cohomology for a Taft algebra, in particular, the Sweedler algebra H_4.
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Other Information
http://mathoverflow.net/questions/12782/tatecohomologyviastablecategories
Salomonsson on products in negative Tate cohomology: http://front.math.ucdavis.edu/1007.3355
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