Lemma 28.4.5 (01OT)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 28: Properties of Schemes
Section 28.4: Types of schemes defined by properties of rings
Lemma 28.4.5 (cite)

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Lemma 28.4.5. The following properties of a ring $R$ are local.

(Cohen-Macaulay.) The ring $R$ is Noetherian and CM, see Algebra, Definition 10.104.6.
(Regular.) The ring $R$ is Noetherian and regular, see Algebra, Definition 10.110.7.
(Absolutely Noetherian.) The ring $R$ is of finite type over $Z$ .
Add more here as needed.¹

Proof. Omitted. $\square$

[1] But we only list those properties here which we have not already dealt with separately somewhere else.

Comments (2)

Comment #98 by Pieter Belmans on December 01, 2012 at 06:31

It should be Cohen-Macaulay, not Macauley.

Comment #101 by Johan on December 04, 2012 at 14:33

Fixed. Thanks!

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