Lemma 74.11.29 (042C)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 74: Descent and Algebraic Spaces
Section 74.11: Descending properties of morphisms in the fpqc topology
Lemma 74.11.29 (cite)

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Lemma 74.11.29. The property $\mathcal{P}(f) =$“$f$ is finite locally free” is fpqc local on the base.

Proof. Being finite locally free is equivalent to being finite, flat and locally of finite presentation (Morphisms of Spaces, Lemma 67.46.6). Hence this follows from Lemmas 74.11.23, 74.11.13, and 74.11.10. $\square$

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