Suppose $G$ is a pro-$p$ group and $M$ is a discrete $p$-primary module not necessarily finite. Suppose the $p$-cohomological dimension of $G$ is $n$. Can one conclude $$ H^n(G,M) \neq 0? $$
This is fairly easy to see when $M$ is finite..
2026-03-26 19:20:07.1774552807
Vanishing of a Galois cohomology of a pro-$p$ group
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