Lemma 35.23.22 (02L9)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 35: Descent
Section 35.23: Properties of morphisms local in the fpqc topology on the target
Lemma 35.23.22 (cite)

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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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