Definition 17.17.3. Let $(X, \mathcal{O}_ X)$ be a ringed space. Let $x \in X$. An $\mathcal{O}_ X$-module $\mathcal{F}$ is *flat at $x$* if $\mathcal{F}_ x$ is a flat $\mathcal{O}_{X, x}$-module.

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