Holmstrom Group cohomology

Group cohomology

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Group cohomology

Chromatic filtration

For something related to group cohomology in terms of monad cohomology, see gmail email by Johannes Huebschmann Nov 2008

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Group cohomology

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 $G$-sets. Abelian sheaves on this site are equivalent to left $G$-modules. For a left G-module $A$, the cohomology group $H^q(G, A)$ can be expressed as the sheaf cohomology group $H^q(e, Hom_G(-, A))$, where $e$ is the one-point set with its unique structure of a left $G$-set. There is also a more general expression for a subgroup of $G$.

For continuous group cohomology of a profinite group (Tate cohomology?), one has a similar story. See Tamme p. 55-56, 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.

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There is also a notion of group hypercohomology (“coeffs in a complex of modules”).

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Group cohomology

RT, CT (Category theory)

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Group cohomology

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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Group cohomology

nlab, a bit nonclassical

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Group cohomology

http://mathoverflow.net/questions/674/what-is-a-cup-product-in-group-cohomology-and-how-does-it-relate-to-other-branch

http://mathoverflow.net/questions/72810/the-relationship-between-group-cohomology-and-topological-cohomology-theories

http://mathoverflow.net/questions/10879/intuition-for-group-cohomology

http://mathoverflow.net/questions/52099/cohomology-theory-for-algebraic-groups

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Group cohomology

Here is something: http://www.math.uiuc.edu/K-theory/0056

http://mathoverflow.net/questions/37214/why-arent-there-more-classifying-spaces-in-number-theory

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Group cohomology

http://mathoverflow.net/questions/117070/evens-norm-as-a-derived-functor mentions also several other important maps in groups cohomology, inflation etc.

nLab page on Group cohomology