Shifted Poisson structures and deformation quantization

Abstract : 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.
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Journal of topology, Oxford University Press, 2017, 10 (2), pp.483-584. 〈10.1112/topo.12012〉
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Dernière modification le : jeudi 21 juin 2018 - 11:02:33

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Damien Calaque, Tony Pantev, Bertrand Toën, Michel Vaquié, Gabriele Vezzosi. Shifted Poisson structures and deformation quantization. Journal of topology, Oxford University Press, 2017, 10 (2), pp.483-584. 〈10.1112/topo.12012〉. 〈hal-01253029v2〉

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