Openness of versality via coherent functors

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.

32 pages, revised Introduction

Cited by in corpus (1)

• Cohomology and base change for algebraic stacks