English

Structures symplectiques et de Poisson sur les champs en cat\'egories

Algebraic Geometry 2018-04-30 v1 Algebraic Topology

Abstract

The purpose of this short note is to present two existence results concerning symplectic and lagrangian structures in the derived setting, in situations where the constructions of [Ca] and [PTVV] do not apply. For this we show that symplectic structures can be constructed out of Calabi-Yau structures on sheaves of dg-categories, or out of \emph{orientations} on sheaves of rigid dg-categories. These results follow from two main theorems: the HKR theorem and the cyclotomic aspect of traces in rigid infty-categories.

Keywords

Cite

@article{arxiv.1804.10444,
  title  = {Structures symplectiques et de Poisson sur les champs en cat\'egories},
  author = {Bertrand Toën},
  journal= {arXiv preprint arXiv:1804.10444},
  year   = {2018}
}

Comments

French, 13 pages