Lemma 35.30.1 (036U)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 35: Descent
Section 35.30: Properties of morphisms local in the smooth topology on the source
Lemma 35.30.1 (cite)

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Lemma 35.30.1. The property $\mathcal{P}(f)=$“$f$ is smooth” is smooth local on the source.

Proof. Combine Lemma 35.26.4 with Morphisms, Lemma 29.34.2 (local for Zariski on source and target), Morphisms, Lemma 29.34.4 (pre-composing), and Lemma 35.14.4 (part (4)). $\square$

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