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In mathematics, group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to elucidate the properties of the group.

3 votes
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104 views

Computing the derived $I$ invariants $D(G\operatorname{Rep})\to D((G/I)\operatorname{Rep})$

In Scholze's paper The Langlands–Kottwitz approach for the modular curve (published version) about $\operatorname{GL}_2$ when he wants to find the relation between the semisimple trace and the usual t …
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3 votes
1 answer
302 views

Projective dimension of group ring

Assume that $G$ is a group and $R$ is a p.i.d. What can we say about the projective dimension of $R[G]$? For example can we say that this dimension is at most $1$ for reductive groups? (I think if $ …
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