Shifted Contact Structures and Their Local Theory

TL;DR

This paper introduces shifted contact structures on derived stacks, establishing their local properties and a Darboux-like theorem, advancing the understanding of derived algebraic geometry.

Contribution

It defines shifted contact structures on derived stacks and proves a Darboux-like theorem for negatively shifted contact derived schemes, expanding the theoretical framework.

Findings

Defined shifted contact structures on derived stacks

Proved a Darboux-like theorem for negatively shifted contact schemes

Formulated the notion of symplectification in this context

Abstract

In this paper, we formally define the concept of shifted contact structures on derived (Artin) stacks and study their local properties in the context of derived algebraic geometry. In this regard, for negatively shifted contact derived $\mathbb{K}$-schemes, we develop a Darboux-like theorem and formulate the notion of symplectification.