On the Bezrukavnikov–Kaledin quantization of symplectic varieties in characteristic p

Abstract

We prove that after inverting the Planck constant $h$ , the Bezrukavnikov–Kaledin quantization $(X, {\mathcal {O}}_h)$ of symplectic variety $X$ in characteristic $p$ with $H^2(X, {\mathcal {O}}_X) =0$ is Morita equivalent to a certain central reduction of the algebra of differential operators on $X$ .