Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 137-182 |
| Number of pages | 46 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Volume | 2017 |
| Issue number | 722 |
| DOIs | |
| State | Published - Jan 2017 |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics