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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