Lemma 82.4.8. Let $S$ be a scheme. Let $f : X \to Y$ be a proper morphism of algebraic spaces. Let $\overline{y} \to Y$ be a geometric point.

For a torsion abelian sheaf $\mathcal{F}$ on $X_{\acute{e}tale}$ we have $(R^ nf_*\mathcal{F})_{\overline{y}} = H^ n_{\acute{e}tale}(X_{\overline{y}}, \mathcal{F}_{\overline{y}})$.

For $E \in D^+(X_{\acute{e}tale})$ with torsion cohomology sheaves we have $(R^ nf_*E)_{\overline{y}} = H^ n_{\acute{e}tale}(X_{\overline{y}}, E_{\overline{y}})$.

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