On Shifted Contact Derived Artin Stacks

TL;DR

This work extends shifted contact geometry from derived schemes to derived Artin stacks, establishing a $k<0$ Darboux-type atlas and a canonical symplectification for negatively shifted contact derived Artin stacks. It develops a suite of constructions for contact derived stacks using cotangent and twisted cotangent stacks and shifted prequantization, and provides explicit Darboux-form atlases and symplectifications in the Artin setting. The paper also offers concrete examples, including shifted 1-jet stacks and prequantization-driven contact structures on key moduli spaces such as LocSys$_G(C)$ and Bun$_G(C)$. Overall, it strengthens the bridge between contact and symplectic geometry in the derived stack framework and expands practical tools for constructing and studying shifted geometric structures.

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.

Theorems & Definitions (49)

• Theorem 1.1
• Theorem 1.2
• Theorem 1.3
• Definition 2.1
• Definition 2.2
• Definition 2.3
• Definition 2.4
• Definition 2.5
• Theorem 2.8
• Proposition 2.9