Group cohomology

General Introduction
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Search results
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Online References
nlab, a bit nonclassical
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Paper References
Godement, Sem Bourbaki exp 90: Cohomology of discontinuous groups
Various things in the folder Group and Galois cohomology, including book by Brown and historical survey by MacLane.
Cam Studies in Adv Math 31: Representations and cohomology II, by Benson, excellent. What about vol I??
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Definition
One can define group cohomology as a sheaf cohomology. For this, one considers the site given by the canonical topology on the category of left sets. Abelian sheaves on this site are equivalent to left modules. For a left Gmodule , the cohomology group can be expressed as the sheaf cohomology group , where is the onepoint set with its unique structure of a left set. There is also a more general expression for a subgroup of .
For continuous group cohomology of a profinite group (Tate cohomology?), one has a similar story. See Tamme p. 5556, for details.
One can view group cohomology as a functor from modules with a group action to abelian groups. See Baues: Homotopy types, section 5.
There is also a notion of group hypercohomology ("coeffs in a complex of modules").
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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
Here is something: K0056
http://mathoverflow.net/questions/37214/whyarenttheremoreclassifyingspacesinnumbertheory
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Computations and Examples
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History and Applications
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Some Research Articles
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Other Information
http://mathoverflow.net/questions/10879/intuitionforgroupcohomology
http://mathoverflow.net/questions/52099/cohomologytheoryforalgebraicgroups
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