Lemma 59.91.3 (0A3S)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 59: Étale Cohomology
Section 59.91: The proper base change theorem
Lemma 59.91.3 (cite)

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Lemma 59.91.3. 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 59.91.2. $\square$

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