Talk:Artin's criterion

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
Low	This article has been rated as Low-priority on the project's priority scale.

	This article was reviewed by member(s) of WikiProject Articles for creation. The project works to allow users to contribute quality articles and media files to the encyclopedia and track their progress as they are developed. To participate, please visit the project page for more information.Articles for creationWikipedia:WikiProject Articles for creationTemplate:WikiProject Articles for creationAfC articles
	This article was accepted from this draft on 1 March 2017 by reviewer GeoffreyT2000 (talk · contribs).

This page was nominated for deletion on 25 January 2016. The result of the discussion was keep.

Notes edit

Latest comment: 3 years ago2 comments1 person in discussion

Artin's first paper is available in Global Analysis: Papers in Honor of K. Kodaira (PMS-29), pages 21-72 — Preceding unsigned comment added by Wundzer (talk • contribs) 14:39, 17 June 2020 (UTC)Reply
Artin approximation pdf - https://www.ams.org/journals/bull/2017-54-04/S0273-0979-2017-01579-0/supplementary-information/S0273-0979-2017-01579-0-original-version.pdf
Associated lectures online - https://library.cirm-math.fr/Record.htm?idlist=7&record=19277720124910959029 - Commutative algebra for Artin approximation - Part 1
Commutative algebra for Artin approximation - Part 2 - https://library.cirm-math.fr/Record.htm?idlist=7&record=19277747124910959299
Commutative algebra for Artin approximation - Part 3 - https://library.cirm-math.fr/Record.htm?idlist=7&record=19277759124910959319 — Preceding unsigned comment added by Wundzer (talk • contribs) 19:49, 18 June 2020 (UTC)Reply

Artin's criterion should include all of his criteria, not just for algebraic spaces. This means representability of moduli functors as stacks, etc.

Versal deformations and algebraic stacks - Representability of algebraic stacks - https://link.springer.com/article/10.1007/BF01390174
Algebraic approximation of structures over complete local rings
Algebraization of formal moduli. I
Theoremes de representabilite pour les espaces algebriques