  Let $A$ be a central quantization of an affine Poisson variety $X$ over a
field of characteristic $p>0.$ We show that the completion of $A$ with respect
to a closed point $y\in X$ is isomorphic to the tensor product of the Weyl
algebra with a local Poisson algebra. This result can be thought of as a
positive characteristic analogue of results of Losev and Kaledin about slice
algebras of quantizations in characteristic 0.
