The Stacks project

Definition 38.21.1. Let $X \to S$ be a morphism of schemes. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module. We say that the universal flattening of $\mathcal{F}$ exists if the functor $F_{flat}$ defined in Situation 38.20.13 is representable by a scheme $S'$ over $S$. We say that the universal flattening of $X$ exists if the universal flattening of $\mathcal{O}_ X$ exists.

Comments (2)

Comment #4155 by Laurent Moret-Bailly on

Suggested example where the universal flattening does not exist: , where . Namely, for all , while .

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  • 4 comment(s) on Section 38.21: Flattening stratifications

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View Definition 38.21.1 as pdf