Lemma 66.21.1 (03G6)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 66: Properties of Algebraic Spaces
Section 66.21: The structure sheaf of an algebraic space
Lemma 66.21.1 (cite)

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Lemma 66.21.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. The rule $U \mapsto \Gamma (U, \mathcal{O}_ U)$ defines a sheaf of rings on $X_{\acute{e}tale}$.

Proof. Immediate from the definition of a covering and Descent, Lemma 35.8.1. $\square$

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