Openness of versality via coherent functors

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13 Scopus citations


We give a proof of openness of versality using coherent functors. As an application, we streamline Artin's criterion for algebraicity of a stack. We also introduce multi-step obstruction theories, employing them to produce obstruction theories for the stack of coherent sheaves, the Quot functor, and spaces of maps in the presence of non-flatness.

Original languageEnglish (US)
Pages (from-to)137-182
Number of pages46
JournalJournal fur die Reine und Angewandte Mathematik
Issue number722
StatePublished - Jan 2017

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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