The Stacks project

Definition 67.47.7. Let $S$ be a scheme. Let $X$ and $Y$ be algebraic spaces over $S$ with $|X|$ and $|Y|$ irreducible. We say $X$ and $Y$ are birational if $X$ and $Y$ are isomorphic in the category of irreducible algebraic spaces over $S$ and dominant rational maps.

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