Suppose I have a global field $K$ and a Galois extension $L/K$ of Galois group $G$. It is often written without proofs (it seems that this is a very common statement) that for every $G$-module $M$ of permutation, one has $\mathrm{Sha}(G,M)=0$. Do you have any reference for this ? or a proof (if it's not too long) ?