The Stacks project

Lemma 35.23.22. The property $\mathcal{P}(f) =$“$f$ is integral” is fpqc local on the base.

Proof. An integral morphism is the same thing as an affine, universally closed morphism. See Morphisms, Lemma 29.44.7. Hence the lemma follows on combining Lemmas 35.23.3 and 35.23.18. $\square$

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