# On the center of the ring of differential operators on a smooth variety over Z/p^nZ.

SPEAKER: Allen J. Stewart

TITLE: On the center of the ring of differential operators on a smooth variety over Z/p^nZ.

ABSTRACT We compute the center of the ring of crystalline differential operators on a smooth variety over $mathbb{Z}/p^nmathbb{Z}$ confirming a conjecture of Kaledin. More generally, given an associative algebra $A_0$ over $mathbb{F}_p$ and its flat deformation $A_n$ over $mathbb{Z}/p^{n+1}mathbb{Z}$ 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 $A_0$