Tate cohomology
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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 Tate-Hochschild 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 Tate-Hochschild cohomology of A that was presented by Bergh and Jorgensen. We introduce cup products that make the Tate and Tate-Hochschild cohomology of A become graded rings. We establish the relationship between these rings, which turns out to be similar to that in the ordinary non-Tate cohomology case. As an example, we explicitly compute the Tate-Hochschild cohomology for a finite dimensional (cyclic) group algebra. In another example, we compute both the Tate and Tate-Hochschild cohomology for a Taft algebra, in particular, the Sweedler algebra H_4.
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Other Information
http://mathoverflow.net/questions/12782/tate-cohomology-via-stable-categories
Salomonsson on products in negative Tate cohomology: http://front.math.ucdavis.edu/1007.3355
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