Lemma 70.10.4. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$ and let $G$ be a finite group acting freely on $X$. Set $Y = X/G$ as in Properties of Spaces, Lemma 64.34.1. For $y \in |Y|$ the following are equivalent
$y$ is in the schematic locus of $Y$, and
there exists an affine open $U \subset X$ containing the preimage of $y$.