On the center of the ring of differential operators on a smooth variety over \bZ/p^n\bZ

Abstract

We compute the center of the ring of PD differential operators on a smooth variety over \bZ/p^n\bZ confirming a conjecture of Kaledin. More generally, given an associative algebra $A_0$ over \bF_p and its flat deformation $A_n$ over \bZ/p^{n+1}\bZ we prove that under a certain non-degeneracy condition the center of $A_n$ is isomorphic to the ring of length $n+1$ Witt vectors over the center of $A_0$.Comment: 16 page