Hochschild cohomology of deformation quantizations over $\mathbb{Z}\mathrm{/}{p}^n\mathbb{Z}$

Let X be a an affine smooth symplectic variety over $\mathbb{Z}\mathrm{/}p\mathbb{Z},$ and A be its deformation quantization over the p-adic integers. We prove that for all $n\ge 1,$ the Hochschild cohomogy of $A\mathrm{/}{p}^{n}A$ is isomorphic to the de Rham-Witt complex of X over $\mathbb{Z}\mathrm{/}{p}^n\mathbb{Z}$. We also compute centers of deformations of certain affine Poisson varieties over $\mathbb{Z}\mathrm{/}p\mathbb{Z}\mathrm{.}$