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

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 $X$.