I'm trying to learn the basics of Galois cohomology. If $k$ is a perfect field and $k^s$ is a separable closure, and $A$ is a finite group, how do you compute $H^1(\text{Gal}(k^s/k),A)=H^1(k,A)$?
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Is the action on $A$ trivial? If so you're asking for homomorphisms from the absolute Galois group to $A$ and I don't know what there is to say about this in general without more information about one or the other. – Qiaochu Yuan Aug 11 '20 at 03:56