Lemma 67.45.6 (0414)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 67: Morphisms of Algebraic Spaces
Section 67.45: Integral and finite morphisms
Lemma 67.45.6 (cite)

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Lemma 67.45.6. A finite morphism of algebraic spaces is integral. An integral morphism of algebraic spaces which is locally of finite type is finite.

Proof. In both cases the morphism is representable, and you can check the condition after a base change by an affine scheme mapping into $Y$ , see Lemmas 67.45.3. Hence this lemma follows from the same lemma for the case of schemes, see Morphisms, Lemma 29.44.4. $\square$

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