Quantization of line bundles on Lagrangian subvarieties
arXiv:1403.3493
Abstract
We apply the technique of formal geometry to give a necessary and sufficient condition for a line bundle supported on a smooth Lagrangian subvariety to deform to a sheaf of modules over a fixed deformation quantization of the structure sheaf of an algebraic symplectic variety.
some minor improvements, including references to the complex analytic case