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

Part of: Arithmetic problems. Diophantine geometry (Co)homology theory Rings and algebras arising under various constructions

Published online by Cambridge University Press:  31 October 2012

Allen Stewart  and
Vadim Vologodsky
Allen Stewart
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USA (email: [email protected])
Vadim Vologodsky
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403, USA (email: [email protected])
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Abstract

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We 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 algebra A0 over ℤp and its flat deformation An over ℤ/pn+1ℤ, we prove that under a certain non-degeneracy condition, the center of An is isomorphic to the ring of length-(n+1) Witt vectors over the center of A0.

Keywords

deformations of algebrasPoisson algebrasWitt vectors

MSC classification

Secondary: 14F10: Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 14G17: Positive characteristic ground fields 16S34: Group rings , Laurent polynomial rings 16S80: Deformations of rings
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 1 , January 2013 , pp. 63 - 80
Copyright
Copyright © The Author(s) 2012

References

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