Lemma 59.91.2. Let (A, I) be a henselian pair. Let f : X \to \mathop{\mathrm{Spec}}(A) be a proper morphism of schemes. Let i : Z \to X be the closed immersion of X \times _{\mathop{\mathrm{Spec}}(A)} \mathop{\mathrm{Spec}}(A/I) into X. For any sheaf \mathcal{F} on X_{\acute{e}tale} we have \Gamma (X, \mathcal{F}) = \Gamma (Z, i_{small}^{-1}\mathcal{F}).
Proof. This follows from Lemma 59.82.2 and 59.91.1 and the fact that any scheme finite over X is proper over \mathop{\mathrm{Spec}}(A). \square
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