Definition 77.11.3. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$ 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 $Y$ in dimensions $\geq n$ if the equivalent conditions of Lemma 77.11.2 are satisfied.
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