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