Lemma 66.18.6 (04JS)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 66: Properties of Algebraic Spaces
Section 66.18: The étale site of an algebraic space
Lemma 66.18.6 (cite)

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Lemma 66.18.6. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$ . The functor $X_{affine, {\acute{e}tale}} \to X_{\acute{e}tale}$ is special cocontinuous and induces an equivalence of topoi from $\mathop{\mathit{Sh}}\nolimits (X_{affine, {\acute{e}tale}})$ to $\mathop{\mathit{Sh}}\nolimits (X_{\acute{e}tale})$ .

Proof. Omitted. Hint: compare with the proof of Topologies, Lemma 34.4.11. $\square$

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