The Stacks project

Lemma 82.4.9. Let $k \subset k'$ be an extension of separably closed fields. Let $X$ be a proper algebraic space over $k$. Let $\mathcal{F}$ be a torsion abelian sheaf on $X$. Then the map $H^ q_{\acute{e}tale}(X, \mathcal{F}) \to H^ q_{\acute{e}tale}(X_{k'}, \mathcal{F}|_{X_{k'}})$ is an isomorphism for $q \geq 0$.

Proof. This is a special case of Theorem 82.4.6. $\square$


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