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 an algebraically closed field, and $X$ a connected smooth projective curve over $X$. Let $F$ be the function field of $k$. Let $G$ be an algebraic group over $k$ (assume that it is smooth, ...