Shifted cotangent stacks are shifted symplectic

2016/12/31 by Damien Calaque · 29 citations
Mathematics · #Algebraic Geometry and Number Theory #Carry (investment) #Geometric and Algebraic Topology #Geometry #Homotopy and Cohomology in Algebraic Topology #Lagrangian #Mathematics #Non canonical #Pure mathematics #Symplectic geometry #Trigonometric functions #math.AG #math.AT #math.SG

paper · pdf · doi:10.5802/afst.1593

published in Annales de la faculté des sciences de Toulouse Mathématiques 28(1), 67-90 (Cellule MathDoc/CEDRAM) · 16 pages. Minor corrections. To appear in Annales de la Faculté des Sciences de Toulouse

arxiv created 2017/03/08 · openalex publication_date 2019/03/20 · arxiv updated 2019/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove that shifted cotangent stacks carry a canonical shifted symplectic structure. We also prove that shifted conormal stacks carry a canonical Lagrangian structure. These results were believed to be true, but no written proof was available in the Artin case.

Citations

• Quasi-Hamiltonian reduction via classical Chern–Simons theory
• Derived coisotropic structures II: stacks and quantization
• Derived coisotropic structures I: affine case

Cited by

• Shifted Symplectic Fibrations and Derived Thurston Theorem
• Equivariant Contact Darboux Quotients and Perversely Categorified Legendrian Correspondences

Related

• Shifted cotangent bundles, symplectic groupoids and deformation to the normal cone
• Shifted Symplectic Structures
• The derived moduli stack of shifted symplectic structures
• Shifted symplectic structures
• Shifted symplectic pushforwards