Lemma 83.4.3. Let $A$ be a henselian local ring. Let $X$ be an algebraic space over $A$ such that $f : X \to \mathop{\mathrm{Spec}}(A)$ be a proper morphism. Let $X_0 \subset X$ be the fibre of $f$ over the closed point. For any sheaf $\mathcal{F}$ on $X_{\acute{e}tale}$ we have $\Gamma (X, \mathcal{F}) = \Gamma (X_0, \mathcal{F}|_{X_0})$.

**Proof.**
This is a special case of Lemma 83.4.2.
$\square$

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## Comments (2)

Comment #7738 by Laurent Moret-Bailly on

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