Lemma 76.47.4 (06C2)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 76: More on Morphisms of Spaces
Section 76.47: Perfect morphisms
Lemma 76.47.4 (cite)

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Lemma 76.47.4. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$ . The following are equivalent

$f$ is flat and perfect, and
$f$ is flat and locally of finite presentation.

Proof. Omitted. Hint: Use the schemes version of this lemma, see More on Morphisms, Lemma 37.61.5. $\square$

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