Structures symplectiques et de Poisson sur les champs en catégories

Abstract

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 \emph{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.

arXiv commentFrench, 13 pages

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Cited by in corpus (6)

• Pre-Calabi-Yau structures and moduli of representations
• Relative critical loci and quiver moduli
• Calabi-Yau structures for multiplicative preprojective algebras
• Moduli of $p$-adic representations of a profinite group
• Moduli of $\ell$-adic pro-étale local systems for smooth non-proper schemes
• Calabi-Yau structures on (quasi-)bisymplectic algebras