Fedosov quantization in positive characteristic

Abstract

We study the problem of deformation quantization for (algebraic) symplectic manifolds over a base field of positive characteristic. We prove a reasonably complete classification theorem for one class of such quantizations; in the course of doing it, we also introduce a notion of a restricted Poisson algebra – the Poisson analog of the standard notion of a restricted Lie algebra – and we prove a version of the Darboux Theorem valid in the positive characteristic setting.