Definition 66.31.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Let $\mathcal{F}$ be a quasi-coherent sheaf on $X$.

Let $x \in |X|$. We say $\mathcal{F}$ is

*flat at $x$ over $Y$*if the equivalent conditions of Lemma 66.31.1 hold.We say $\mathcal{F}$ is

*flat over $Y$*if $\mathcal{F}$ is flat over $Y$ at all $x \in |X|$.

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