The Stacks project

Lemma 59.92.1. Let $K/k$ be an extension of separably closed fields. Let $X$ be a proper scheme over $k$. Let $\mathcal{F}$ be a torsion abelian sheaf on $X_{\acute{e}tale}$. 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. Looking at stalks we see that this is a special case of Theorem 59.91.11. $\square$

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