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Fedosov quantization in positive characteristic

Authors: R. Bezrukavnikov and D. Kaledin
Journal: J. Amer. Math. Soc. 21 (2008), 409-438
MSC (2000): Primary 14M99
Published electronically: November 26, 2007
MathSciNet review: 2373355
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Abstract: We study the problem of deformation quantization for (algebraic) symplectic manifolds over a base field of positive characteristic. We prove a reasonably complete classification theorem for one class of such quantizations; in the course of doing it, we also introduce a notion of a restricted Poisson algebra – the Poisson analog of the standard notion of a restricted Lie algebra – and we prove a version of the Darboux Theorem valid in the positive characteristic setting.

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Additional Information

R. Bezrukavnikov
Affiliation: Department of Mathematics, Massachusets Institute of Technology, Cambridge, Massachusetts 02139
MR Author ID: 347192

D. Kaledin
Affiliation: Steklov Institute, Gubkina 8, Moscow, 119991, Russia
MR Author ID: 634964

Received by editor(s): October 7, 2005
Published electronically: November 26, 2007
Additional Notes: The first author was partially supported by NSF grant DMS-0071967.
The second author was partially supported by CRDF grant RM1-2694-MO05.
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.