A note on étale atlases for Artin stacks and Lie groupoids, Poisson structures and quantisation

DOI10.1016/j.geomphys.2024.105266zbMATH Open1548.531MaRDI QIDQ6596135

Jonathan Paul Pridham

Publication date: 2 September 2024

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

Lie algebroidsPoisson structuresArtin stacks

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Deformation quantization, star products (53D55) Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects) (18F20) Local structure of morphisms in algebraic geometry: étale, flat, etc. (14B25) Stacks and moduli problems (14D23) Fundamental constructions in algebraic geometry involving higher and derived categories (homotopical algebraic geometry, derived algebraic geometry, etc.) (14A30)

Cites Work

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• Presenting higher stacks as simplicial schemes
• Unifying derived deformation theories
• Versal deformations and algebraic stacks
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• Quantisation of derived Lagrangians
• A differential graded model for derived analytic geometry
• Lagrangian structures on mapping stacks and semi-classical TFTs
• Higher Poisson Brackets and Differential Forms
• C ∞ -Schemes
• Deformation quantisation for $(-1)$-shifted symplectic structures and vanishing cycles
• Shifted Poisson and symplectic structures on derived N-stacks
• Shifted Poisson structures and deformation quantization
• Homotopical algebraic geometry. II. Geometric stacks and applications
• Simplicial homotopy theory

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