Lemma 38.11.2. Let $f : X \to S$ be a morphism of schemes. Let $U \subset S$ be open. Assume

$f$ is locally of finite type and flat,

$U \subset S$ is retrocompact and scheme theoretically dense,

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

Then $f$ is of locally of finite presentation.

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