On Shifted Contact Derived Artin Stacks

TL;DR

This paper extends the theory of shifted contact structures from derived schemes to derived Artin stacks, establishing Darboux atlases, symplectifications, and new constructions within derived contact geometry.

Contribution

It generalizes shifted contact structures to derived Artin stacks and provides foundational results and constructions for this extended framework.

Findings

Existence of contact Darboux atlases for $k$-shifted contact derived Artin stacks

Canonical description of symplectification of such stacks

New constructions of contact derived stacks using cotangent stacks and prequantization

Abstract

This is a sequel of our previous work, arXiv:2209.09686, on the development of derived contact geometry, in which we formally introduced shifted contact structures on derived stacks and proved some results for $k$-shifted contact derived schemes, with $k<0$. In this paper, we extend these results from derived schemes to derived Artin stacks. In brief, we first show that for $k<0$, every $k$-shifted contact derived Artin stack admits a contact Darboux atlas. Secondly, we canonically describe the symplectification of a derived Artin stack equipped with a $k$-shifted contact structure, where $k<0$. Lastly, we give several constructions of contact derived stacks using certain cotangent stacks and shifted prequantization structures.