English

On Shifted Contact Derived Artin Stacks

Algebraic Geometry 2025-03-21 v3

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 kk-shifted contact derived schemes, with k<0k<0. In this paper, we extend these results from derived schemes to derived Artin stacks. In brief, we first show that for k<0k<0, every kk-shifted contact derived Artin stack admits a contact Darboux atlas. Secondly, we canonically describe the symplectification of a derived Artin stack equipped with a kk-shifted contact structure, where k<0k<0. Lastly, we give several constructions of contact derived stacks using certain cotangent stacks and shifted prequantization structures.

Cite

@article{arxiv.2401.03334,
  title  = {On Shifted Contact Derived Artin Stacks},
  author = {Kadri İlker Berktav},
  journal= {arXiv preprint arXiv:2401.03334},
  year   = {2025}
}

Comments

V03: 27 Pages; Example 2.21 and Theorem 3.7 revised; corrections and edits suggested by an anonymous referee; final version to paper in Higher Structures. Comments are welcome! sequel to arXiv:2209.09686

R2 v1 2026-06-28T14:10:20.882Z