The Stacks project

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

  1. $f$ is flat and perfect, and

  2. $f$ 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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