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The Stacks project

Lemma 38.18.4. Let f : X \to S be a finite type morphism of schemes. Let \mathcal{F} be a finite type quasi-coherent \mathcal{O}_ X-module. Assume \mathcal{F} is flat over S. In this case \mathcal{F} is pure relative to S if and only if \mathcal{F} is universally pure relative to S.

Proof. Immediate consequence of Lemma 38.18.3 and the definitions. \square


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