  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.
