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The Stacks project

Definition 67.47.1. Let S be a scheme. Let X, Y be algebraic spaces over S.

  1. Let f : U \to Y, g : V \to Y be morphisms of algebraic spaces over S defined on dense open subspaces U, V of X. We say that f is equivalent to g if f|_ W = g|_ W for some dense open subspace W \subset U \cap V.

  2. A rational map from X to Y is an equivalence class for the equivalence relation defined in (1).

  3. Given morphisms X \to B and Y \to B of algebraic spaces over S we say that a rational map from X to Y is a B-rational map from X to Y if there exists a representative f : U \to Y of the equivalence class which is a morphism over B.


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