Quantization of restricted Lagrangian subvarieties in positive characteristic
arXiv:2106.09912 · doi:10.1016/j.aim.2022.108760
Abstract
Bezrukavnikov and Kaledin introduced quantizations of symplectic varieties X in positive characteristic which endow the Poisson bracket on X with the structure of a restricted Lie algebra. We consider deformation quantization of line bundles on Lagrangian subvarieties Y of X to modules over such quantizations. If the ideal sheaf of Y is a restricted Lie subalgebra of the structure sheaf of X, we show that there is a certain cohomology class which vanishes if and only if a line bundle on Y admits a quantization.
24 pages. Final version, to appear in Advances in Mathematics