The Stacks project

Proposition 59.27.4. Let $S$ be a scheme and $\mathcal{F}$ an abelian sheaf on $(\mathit{Sch}/S)_{\acute{e}tale}$. Then $\mathcal{F}|_{S_{\acute{e}tale}}$ is a sheaf on $S_{\acute{e}tale}$ and

\[ H^ p_{\acute{e}tale}(S, \mathcal{F}|_{S_{\acute{e}tale}}) = H^ p_{\acute{e}tale}(S, \mathcal{F}) \]

for all $p \geq 0$.

Proof. This is a special case of Lemma 59.20.3. $\square$

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