Lemma 28.7.6 (033M)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 28: Properties of Schemes
Section 28.7: Normal schemes
Lemma 28.7.6 (cite)

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Lemma 28.7.6. Let $X$ be a Noetherian scheme. The following are equivalent:

$X$ is normal, and
$X$ is a finite disjoint union of normal integral schemes.

Proof. This is a special case of Lemma 28.7.5 because a Noetherian scheme has a Noetherian underlying topological space (Lemma 28.5.5 and Topology, Lemma 5.9.2). $\square$

Comments (2)

Comment #6814 by Rubén Muñoz--Bertrand on December 20, 2021 at 12:01

Minor typo: missing closing parenthesis at the end of the proof.

Comment #6956 by Johan on January 21, 2022 at 08:33

Thanks and fixed here.

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