Lemma 82.4.5. Let $S$ be a scheme. Let $f : Y \to X$ be a proper morphism of algebraic spaces over $S$. Let $\overline{x} \to X$ be a geometric point. For any sheaf $\mathcal{F}$ on $Y_{\acute{e}tale}$ the canonical map

$(f_*\mathcal{F})_{\overline{x}} \longrightarrow \Gamma (Y_{\overline{x}}, \mathcal{F}_{\overline{x}})$

is bijective.

Proof. This is a special case of Lemma 82.4.4. $\square$

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).