Lemma 66.37.9. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. There is a maximal open subspace $U \subset X$ such that $f|_ U : U \to Y$ is smooth. Moreover, formation of this open commutes with base change by

morphisms which are flat and locally of finite presentation,

flat morphisms provided $f$ is locally of finite presentation.

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