Definition 17.17.1. Let (X, \mathcal{O}_ X) be a ringed space. An \mathcal{O}_ X-module \mathcal{F} is flat if the functor
\textit{Mod}(\mathcal{O}_ X) \longrightarrow \textit{Mod}(\mathcal{O}_ X), \quad \mathcal{G} \mapsto \mathcal{G} \otimes _\mathcal {O} \mathcal{F}
is exact.
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