Lemma 70.10.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. For $U$ affine and étale over $X$ the set $\mathcal{S}_ X(U)$ is the set of nonzerodivisors in $\mathcal{O}_ X(U)$.

**Proof.**
Follows from Lemma 70.7.5.
$\square$

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