2018/04/27 by Bertrand Toën, Toën, Bertrand · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1804.10444
openalex publication_date 2018/04/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this short note is to present two existence results concerning symplectic and lagrangian structures in the derived setting, in situations where the constructions of [Ca] and [PTVV] do not apply. For this we show that symplectic structures can be constructed out of Calabi-Yau structures on sheaves of dg-categories, or out of orientations on sheaves of rigid dg-categories. These results follow from two main theorems: the HKR theorem and the cyclotomic aspect of traces in rigid infty-categories.