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

By Allen Stewart and Vadim Vologodsky

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

Topics: Mathematics - Algebraic Geometry, Primary 14F10, 14G17, Secondary 16S34, 16S80
Year: 2011
DOI identifier: 10.1112/S0010437X12000462
OAI identifier: oai:arXiv.org:1104.2858
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