Definition 38.20.10. Let $f : X \to S$ be a morphism of schemes which is locally of finite type. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module of finite type. Let $n \geq 0$. We say $\mathcal{F}$ is flat over $S$ in dimensions $\geq n$ if the equivalent conditions of Lemma 38.20.9 are satisfied.

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