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