This paper is the sequel to [PTVV] (IHES Vol. 117, 2013). We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and polyvector 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.

Shifted Poisson structures and deformation quantization / Calaque, Damien; Pantev, Tony; Toen, Bertrand; Vaquié, Michel; Vezzosi, Gabriele. - In: JOURNAL OF TOPOLOGY. - ISSN 1753-8416. - STAMPA. - 10:(2017), pp. 483-584. [10.1112/topo.12012]

Shifted Poisson structures and deformation quantization

VEZZOSI, GABRIELE
2017

Abstract

This paper is the sequel to [PTVV] (IHES Vol. 117, 2013). We develop a general and flexible context for differential calculus in derived geometry, including the de Rham algebra and polyvector 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.
2017
10
483
584
Calaque, Damien; Pantev, Tony; Toen, Bertrand; Vaquié, Michel; Vezzosi, Gabriele
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1070887
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