The Stacks project

Lemma 57.87.3. Let $A$ be a henselian local ring. Let $f : X \to \mathop{\mathrm{Spec}}(A)$ be a proper morphism of schemes. 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 57.87.2. $\square$


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