  In this paper we identify the cotangent to the derived stack of
representations of a quiver $Q$ with the derived moduli stack of modules over
the Ginzburg dg-algebra associated with $Q$. More generally, we extend this
result to finite type dg-categories, to a relative setting as well, and to
deformations of these. It allows us to recover and generalize some results of
Yeung, and leads us to the discovery of seemingly new lagrangian subvarieties
in the Hilbert scheme of points in the plane.
