The Stacks project

Lemma 67.49.7. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$ satisfying the equivalent conditions of Lemma 67.49.1. The normalization morphism $\nu $ factors through the reduction $X_{red}$ and $X^\nu \to X_{red}$ is the normalization of $X_{red}$.

Proof. We may check this étale locally on $X$ and hence reduce to the case of schemes which is Morphisms, Lemma 29.54.2. Some details omitted. $\square$

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