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

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

2011-04-14

arxiv.org/abs/1104.2858v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

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 $A_0$.

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