We show that the map $\operatorname{Br} T \to (\operatorname{Br} T_{\bar k})^{\Gamma_k}$ is surjective for a torus $T$ defined over a field $k$ of characteristic $0$ when $k$ is a local or global field or $T$ is quasi-trivial.
Finiteness of Brauer groups of K3 surfaces in characteristic 2
On the m-torsion Subgroup of the Brauer Group of a Global Field
Integrality at a prime for global fields and the perfect closure of global fields of characteristic p>2
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