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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 $H^{1}(A((t)),T)$?

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    $\begingroup$ What do you mean by "compute" with such abstract $T$? If $A$ has nasty singularities (or even just 2 minimal primes), what kind of answer do you want for $T=\mathbf{G}_m$, for example? $\endgroup$
    – nfdc23
    Commented Sep 27, 2017 at 18:14

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