All Questions

Let $k$ be an algebraically closed field. Let $A$ be a strictly henselian local ring which is a $k$-algebra. Let $T$ a torus over $k((t))$. Can we compute $H^{1}(A((t)),T)$?

Let $K$ be a field and $K^s$ a separable closure of $K$, and let $\mathcal{F}$ be a sheaf on $\mathrm{Spec}(K)$ (in the étale topology). By Grothendieck's Galois Theory, we have the isomorphism $$H_{...