The Stacks project

Definition 38.21.3. Let $X \to S$ be a morphism of schemes. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. We say that $\mathcal{F}$ has a flattening stratification if the functor $F_{flat}$ defined in Situation 38.20.13 is representable by a monomorphism $S' \to S$ associated to a stratification of $S$ by locally closed subschemes. We say that $X$ has a flattening stratification if $\mathcal{O}_ X$ has a flattening stratification.

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