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Fedosov quantization in positive characteristic
Author(s):
R.
Bezrukavnikov;
D.
Kaledin
Journal:
J. Amer. Math. Soc.
21
(2008),
409-438.
MSC (2000):
Primary 14M99
Posted:
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.
References:
-
- [BK1]
- R. Bezrukavnikov and D. Kaledin, Fedosov quantization in algebraic context, Moscow Math. J. 4 (2004), 559-592. MR 2119140 (2006j:53130)
- [BK2]
- R. Bezrukavnikov and D. Kaledin, McKay equivalence for symplectic quotient singularities, Proc. of the Steklov Inst. of Math. 246 (2004), 13-33. MR 2101282 (2006e:14006)
- [BMR]
- R. Bezrukavnikov, I. Mirkovic, and D. Rumynin, Localization of modules for a semisimple Lie algebra in prime characteristic, math.RT/0205144.
- [D]
- M. Demazure, Lectures on
 -Divisible Groups, Lecture Notes in Math. 302, Springer, Berlin-Heidelberg-New York, 1972. MR 0344261 (49:9000) - [DP]
- M. Demazure and P. Gabriel, Groupes Algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs, North-Holland Publishing Co., Amsterdam, 1970. MR 0302656 (46:1800)
- [G]
- J. Giraud, Cohomologie non abélienne, Die Grundlehren der mathematischen Wissenschaften, Band 179, Springer-Verlag, Berlin-New York, 1971. MR 0344253 (49:8992)
- [EGA]
- A. Grothendieck, Éléments de Géométrie Algébrique, III, Publ. Math. IHES 24.
- [K]
- M. Kontsevich, Deformation quantization of algebraic varieties, Lett. Math. Phys. 56 (2001), 271-294. MR 1855264 (2002j:53117)
- [M]
- J. Milne, Étale cohomology, Princeton Math. Series, 33, Princeton U. Press, 1980. MR 559531 (81j:14002)
- [NT]
- R. Nest and B. Tsygan, Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems, Asian J. Math. 5 (2001), 599-635. MR 1913813 (2003k:53126)
- [Y]
- A. Yekutieli, On Deformation Quantization in Algebraic Geometry, Adv. in Math. 198 (2006), 383-432. MR 2183259 (2006j:53131)
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Additional Information:
R.
Bezrukavnikov
Affiliation:
Department of Mathematics, Massachusets Institute of Technology, Cambridge, Massachusetts 02139
Email:
bezrukav@math.mit.edu
D.
Kaledin
Affiliation:
Steklov Institute, Gubkina 8, Moscow, 119991, Russia
DOI:
10.1090/S0894-0347-07-00585-1
PII:
S 0894-0347(07)00585-1
Received by editor(s):
October 7, 2005
Posted:
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.
Copyright of article:
Copyright
2007,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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