Shifted Poisson structures and deformation quantization - CNRS - Centre national de la recherche scientifique Accéder directement au contenu
Article Dans Une Revue Journal of topology Année : 2017

Shifted Poisson structures and deformation quantization

Résumé

This paper is a sequel to [PTVV]. We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and poly-vector fields. We then introduce the formalism of formal derived stacks and prove formal localization and gluing results. These allow us to define shifted Poisson structures on general derived Artin stacks, and prove that the non-degenerate Poisson structures correspond exactly to shifted symplectic forms. Shifted deformation quantization for a derived Artin stack endowed with a shifted Poisson structure is discussed in the last section. This paves the way for shifted deformation quantization of many interesting derived moduli spaces, like those studied in [PTVV] and probably many others.
Fichier principal
Vignette du fichier
derpoiss-afterSubmIHES.pdf (781.11 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01253029 , version 1 (08-01-2016)
hal-01253029 , version 2 (05-10-2017)

Identifiants

Citer

Damien Calaque, Tony Pantev, Bertrand Toën, Michel Vaquié, Gabriele Vezzosi. Shifted Poisson structures and deformation quantization. Journal of topology, 2017, 10 (2), pp.483-584. ⟨10.1112/topo.12012⟩. ⟨hal-01253029v2⟩
345 Consultations
369 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More