Quantization of restricted Lagrangian subvarieties in positive characteristic

Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties X in positive characteristic which endow the Poisson bracket on with structure a restricted Lie algebra. We consider deformation quantization line bundles Lagrangian subvarieties Y to modules over such quantizations. If ideal sheaf is subalgebra X, we show that there certain cohomology class vanishes if only bundle admits quantization.