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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