The Stacks project

74.15 Properties of morphisms local in the fpqc topology on the source

Here are some properties of morphisms that are fpqc local on the source.

Lemma 74.15.1. The property $\mathcal{P}(f)=$“$f$ is flat” is fpqc local on the source.

Proof. Follows from Lemma 74.14.3 using Morphisms of Spaces, Definition 67.30.1 and Descent, Lemma 35.27.1. $\square$

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