Lemma 67.38.7 (05W0)—The Stacks project

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Table of contents
Part 4: Algebraic Spaces
Chapter 67: Morphisms of Algebraic Spaces
Section 67.38: Unramified morphisms
Lemma 67.38.7 (cite)

numberstags

Lemma 67.38.7. If $f$ is unramified at $x$ then $f$ is quasi-finite at $x$ . In particular, an unramified morphism is locally quasi-finite.

Proof. Via a diagram as in Lemma 67.22.1 this translates into Morphisms, Lemma 29.35.10. $\square$

Comments (2)

Comment #3021 by Brian Lawrence on December 13, 2017 at 02:50

Suggested slogan: An unramified morphism is locally quasi-finite.

Comment #3139 by Johan on February 01, 2018 at 18:41

Going to ignore this slogan because it is identical to part of the statement of the lemma.

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