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### Hilbert 90 for algebras

Let $L\diagup K$ be a Galois extension of fields satisfying $\left[L:K\right] < \infty$. Let $B$ be a finite-dimensional (as a $K$-vector space) $K$-algebra. Then, the Galois group $G$ of $L\diagup ...

**11**

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### Explicit Bijection between Central Simple Algebras and twists of $\mathbb P^n$

The automorphism group of the algebra of $n$-dimensional matrices over a field $K$ is $PGL_n(K)$. The automorphism group of $n-1$-dimensional projective space over $K$ is also $PGL_n(K)$. Therefore, ...

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### Galois cohomology groups given by étale cohomology

What are cases when Galois cohomology groups are given by étale cohomology?
Example: $S = Spec(K)$ the spectrum of a field, $F \in Sh(K)$, then $H^p(K, F) = H^p(G_K, F_{\bar{K}})$.
What if $G = ...