Derived deformations of Artin stacks

TL;DR

This paper extends deformation theory to Artin stacks and related structures using simplicial categories, enabling the study of complex automorphisms and higher homotopies in derived deformation problems.

Contribution

It generalizes existing techniques to handle derived deformations with higher automorphisms, including stacks and chain complexes, and introduces a framework for deforming diagrams.

Findings

Deformation problems with higher automorphisms are effectively described.

A new approach for studying deformations of diagrams is proposed.

The methods accommodate homotopies and 2-automorphisms in derived settings.

Abstract

We generalise the techniques of arXiv:0908.1963 to describe derived deformations in simplicial categories. This allows us to consider deformation problems with higher automorphisms, such as chain complexes (which have homotopies) and stacks (which have 2-automorphisms). We also give a general approach for studying deformations of diagrams.