Lemma 74.11.22 (0425)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 74: Descent and Algebraic Spaces
Section 74.11: Descending properties of morphisms in the fpqc topology
Lemma 74.11.22 (cite)

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Lemma 74.11.22. 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 of Spaces, Lemma 67.45.7. Hence the lemma follows on combining Lemmas 74.11.3 and 74.11.16. $\square$

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