Lemma 28.12.2 (0B3C)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 28: Properties of Schemes
Section 28.12: Serre's conditions
Lemma 28.12.2 (cite)

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Lemma 28.12.2. Let $X$ be a locally Noetherian scheme. Then $X$ is regular if and only if $X$ has $(R_ k)$ for all $k \geq 0$ .

Proof. Follows from Lemma 28.9.2 and the definitions. $\square$

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