Talk:Artin's criterion

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

Criteria

 * 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

 * 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

 * 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

Other resources

 * Master's Thesis - http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.132.2930&rep=rep1&type=pdf