Does anyone maybe have a reference to the proof of the following result by Tate?


Let $\Gamma$ be the absolute Galois group of the rationals. Then the second cohomology group (for trivial $\Gamma$-action) H$^2(\Gamma, \mathbb{Q}/\mathbb{Z})$ is trivial.


Unfortunately I couldn't find it online or in the library. Any help would be greatly appreciated!


Kind regards!



Reference request to proof that H$^2(\Gamma, \mathbb{Q}/\mathbb{Z}) = 0$
By the Galois cohomology long exact sequence, this is isomorphic to $\operatorname{H}^3(\Gamma,\mathbb{Z})$, and the vanishing of this is Chapter I, Corollary 4.17 in Milne's *Arithmetic Duality Theorems*.


