Lemma 37.59.5. Let $f : X \to S$ be a morphism of schemes. The following are equivalent

1. $f$ is flat and perfect, and

2. $f$ is flat and locally of finite presentation.

Proof. The implication (2) $\Rightarrow$ (1) is More on Algebra, Lemma 15.82.4. The converse follows from the fact that a pseudo-coherent morphism is locally of finite presentation, see Lemma 37.58.5. $\square$

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