The Stacks project

Lemma 84.4.3. Let $A$ be a henselian local ring. Let $X$ be an algebraic space over $A$ such that $f : X \to \mathop{\mathrm{Spec}}(A)$ is 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 84.4.2. $\square$

Comments (2)

Comment #7738 by Laurent Moret-Bailly on

End of second sentence: I think it should be "is a proper morphism".

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