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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.

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“Sheaf cohomology” of Galois groups

The usual geometric point of view on the Galois group of $F$ is that the Galois group is the etale fundamental group of $\operatorname{Spec} F$. It's possible that you're already aware of this point o …
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