The Stacks project

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:

  1. The morphism $f$ is unramified (resp. G-unramified), and

  2. 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 29.33.2. $\square$


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Comment #1284 by on

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


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