Lemma 37.6.8 (02HE)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 37: More on Morphisms
Section 37.6: Formally unramified morphisms
Lemma 37.6.8 (cite)

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Unramified morphisms are the same as formally unramified morphism that are locally of finite type.

Lemma 37.6.8. Let $f : X \to S$ be a morphism of schemes. The following are equivalent:

The morphism $f$ is unramified (resp. G-unramified), and
the morphism $f$ is locally of finite type (resp. locally of finite presentation) and formally unramified.

Proof. Use Lemma 37.6.7 and Morphisms, Lemma 29.35.2. $\square$

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Comment #1284 by Johan Commelin on January 29, 2015 at 12:11

Suggested slogan: Unramified morphisms are the same as formally unramified morphism that are locally of finite type.

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