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Suppose $G$ is a finite Galois group, and $M$ is an infinite $G$-module. When can I say that $H^1(G, M)$ is finite? I know this not true in general. Is it true under certain assumptions on $M$? To be ...

Note: For experts, to save your time, you can just read the highlighted texts and Eqs directly. The ordinary group 2-cocycle condition: Let us remind the usual so-called homogeneous group 2-cocycle $...

I'm trying to understand how the six functor philosophy applies to representation theory. Consider the category of classifying stacks $BG$ (assume $G$ discrete for simplicity). To every stack we can ...

Let $G$ be a finite group. By a $G$-lattice I mean a finitely generated free abelian group $L$ with an action of $G$. One says that $L$ is a permutation lattice if $L$ has a $\mathbb{Z}$-basis ...