Deriving Deligne-Mumford Stacks with Perfect Obstruction Theories

TL;DR

This paper establishes conditions under which a quasicoherent obstruction theory on a Deligne-Mumford stack can be derived from a connective spectral Deligne-Mumford stack, linking classical and spectral algebraic geometry.

Contribution

It provides a criterion connecting classical obstruction theories with spectral structures on Deligne-Mumford stacks, advancing the understanding of their spectral enhancements.

Findings

Identifies conditions for obstruction theories to originate from spectral stacks

Bridges classical and spectral algebraic geometry frameworks

Enhances the structural understanding of Deligne-Mumford stacks

Abstract

We give conditions for a n-connective quasicoherent obstruction theory on a Deligne-Mumford stack to come from the structure of a connective spectral Deligne-Mumford stack on the underlying topos.