Lemma 70.3.3. Let $S$ be a scheme. Let $X$ be a Noetherian algebraic space over $S$. Let $f : Y \to X$ be a birational proper morphism of algebraic spaces with $Y$ reduced. Let $U \subset X$ be the maximal open over which $f$ is an isomorphism. Then $U$ contains

every point of codimension $0$ in $X$,

every $x \in |X|$ of codimension $1$ on $X$ such that the local ring of $X$ at $x$ is normal (Properties of Spaces, Remark 64.7.6), and

every $x \in |X|$ such that the fibre of $|Y| \to |X|$ over $x$ is finite and such that the local ring of $X$ at $x$ is normal.

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