The Stacks project

Lemma 76.37.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Let $V \subset Y$ be an open subspace. Assume

  1. $f$ is locally of finite type and flat,

  2. $V \to Y$ is quasi-compact and scheme theoretically dense,

  3. $f|_{f^{-1}V} : f^{-1}V \to V$ is locally of finite presentation.

Then $f$ is of locally of finite presentation.

Proof. The proof is identical to the proof of Lemma 76.37.1 except one uses More on Flatness, Lemma 38.11.2. $\square$

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