Legendrian Structures in Derived Geometry

TL;DR

This paper introduces Legendrian structures within derived contact geometry, providing formal definitions, natural constructions, affine models, and a Legendrian-Darboux theorem to advance the understanding of derived contact structures.

Contribution

It formally defines Legendrian structures in derived geometry and proves a Legendrian-Darboux theorem, expanding the theoretical framework of derived contact structures.

Findings

Defined Legendrian structures in derived contact geometry

Constructed natural models for Legendrian structures

Proved a Legendrian-Darboux theorem in this context

Abstract

This is the third installment in a series of papers on the subject of derived contact structures. In this paper, we formally introduce the notion of a Legendrian structure in the derived context and provide natural constructions. We then present affine models and prove a Legendrian-Darboux theorem for the Legendrians in contact derived schemes.