On the center of the ring of differential operators on a smooth variety over ℤ/pnℤ

Abstract

AbstractWe compute the center of the ring of PD differential operators on a smooth variety over ℤ/pnℤ, confirming a conjecture of Kaledin (private communication). More generally, given an associative algebraA0over ℤpand its flat deformationAnover ℤ/pn+1ℤ, we prove that under a certain non-degeneracy condition, the center ofAnis isomorphic to the ring of length-(n+1) Witt vectors over the center ofA0.