Shifted Poisson and symplectic structures on derived N-stacks

Abstract

We show that on a derived Artin N-stack, there is a canonical equivalence between the spaces of n-shifted symplectic structures and non-degenerate n-shifted Poisson structures.

34 pages; v2 details added, several simplifications; v3 further simplifications, Artin details added; v4 several changes (mostly cosmetic, including notation and terminology), Examples 3.31 added (2-shifted structures on BG), final version (to appear in J. Topol.); v5 typos fixed and refs updated; v6 corrected Lemma 3.9 and dependent proofs

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• Shifted Coisotropic Correspondences
• Shifted derived Poisson manifolds associated with Lie pairs
• Quantisation of derived Lagrangians
• A Lagrangian Neighbourhood Theorem for shifted symplectic derived schemes
• Quantisation of derived Poisson structures
• Batalin--Vilkovisky quantization and supersymmetric twists
• Infinitesimal 2-braidings from 2-shifted Poisson structures
• Shifted coisotropic structures for differentiable stacks
• Differentiating $L_{\infty }$ groupoids
• Classical BV formalism for group actions
• Quantization of (-1)-Shifted Derived Poisson Manifolds
• Derived symplectic geometry
• Shifted Poisson structures on higher Chevalley-Eilenberg algebras