On the Bezrukavnikov-Kaledin quantization of symplectic varieties in characteristic $p$

TL;DR

This paper proves that the Bezrukavnikov-Kaledin quantization of symplectic varieties in characteristic p, after inverting the Planck constant, is Morita equivalent to a specific central reduction of differential operator algebras.

Contribution

It establishes a Morita equivalence between the quantization and a central reduction of differential operators in characteristic p.

Findings

Morita equivalence of quantization and differential operators

Inversion of the Planck constant is crucial

Connection to central reductions in algebraic geometry

Abstract

We prove that after inverting the Planck constant $h$ the Bezrukavnikov-Kaledin quantization $(X, \mathcal{O}_h)$ of symplectic variety $X$ in characteristic $p$ is Morita equivalent to a certain central reduction of the algebra of differential operators on $X$.