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^n\mathbb{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\$