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Talk:Artin's criterion

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Notes

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Todo

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

Criteria

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  • 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

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Applications

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  • 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

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