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. $\square$
Post a comment
Your email address will not be published. Required fields are marked.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
All contributions are licensed under the GNU Free Documentation License.
Comments (0)