On the local structure of quantizations in characteristic p
  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. 
Akaki Tikaradze
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