Talk:Artin's criterion
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Notes
[edit]- 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)
- 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)
Todo
[edit]Artin's criterion should include all of his criteria, not just for algebraic spaces. This means representability of moduli functors as stacks, etc.
Criteria
[edit]- 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
Extensions
[edit]- Condrad, De Jong - http://math.stanford.edu/~conrad/papers/approx.pdf
- Hall, Rydh - https://www.math.arizona.edu/~jackhall/papers/artin_crit.pdf
- Flenner - Ein Kriterium f¨ur die Offenheit der Versalit¨at,
- Lurie - page 61 of DAG XIV http://people.math.harvard.edu/~lurie/papers/DAG-XIV.pdf
- or page 1289 of http://people.math.harvard.edu/~lurie/papers/DAG-XIV.pdf
Applications
[edit]- Construction of moduli stack of elliptic curves - Deligne Rappoport
- Constrution of moduli of pointed curves (Knudson's thesis)
- Hom stacks - https://arxiv.org/abs/math/0503358