Lemma 67.45.11 (0CZ2)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 67: Morphisms of Algebraic Spaces
Section 67.45: Integral and finite morphisms
Lemma 67.45.11 (cite)

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Lemma 67.45.11. Let $S$ be a scheme. Let $X_ i \to Y$ , $i = 1, \ldots , n$ be finite morphisms of algebraic spaces over $S$ . Then $X_1 \amalg \ldots \amalg X_ n \to Y$ is finite too.

Proof. Follows from the case of schemes (Morphisms, Lemma 29.44.13) by étale localization. $\square$

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