Relative Calabi-Yau structures II: Shifted Lagrangians in the moduli of objects

Abstract

We show that a Calabi-Yau structure of dimension $d$ on a smooth dg category $C$ induces a symplectic form of degree $2-d$ on the moduli space of objects $M_C$. We show moreover that a relative Calabi-Yau structure on a dg functor $C\to D$ compatible with the absolute Calabi-Yau structure on $C$ induces a Lagrangian structure on the corresponding map of moduli $M_D\to M_C$.

33 pages, comments welcome

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