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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Fedosov quantization in positive characteristic
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by R. Bezrukavnikov and D. Kaledin PDF
J. Amer. Math. Soc. 21 (2008), 409-438 Request permission

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
  • R. Bezrukavnikov and D. Kaledin, Fedosov quantization in algebraic context, Mosc. Math. J. 4 (2004), no. 3, 559–592, 782 (English, with English and Russian summaries). MR 2119140, DOI 10.17323/1609-4514-2004-4-3-559-592
  • R. V. Bezrukavnikov and D. B. Kaledin, McKay equivalence for symplectic resolutions of quotient singularities, Tr. Mat. Inst. Steklova 246 (2004), no. Algebr. Geom. Metody, Svyazi i Prilozh., 20–42 (Russian, with Russian summary); English transl., Proc. Steklov Inst. Math. 3(246) (2004), 13–33. MR 2101282
  • [BMR]BMR R. Bezrukavnikov, I. Mirković, and D. Rumynin, Localization of modules for a semisimple Lie algebra in prime characteristic, math.RT/0205144.
  • Michel Demazure, Lectures on $p$-divisible groups, Lecture Notes in Mathematics, Vol. 302, Springer-Verlag, Berlin-New York, 1972. MR 0344261
  • Michel Demazure and Pierre Gabriel, Groupes algĂ©briques. Tome I: GĂ©omĂ©trie algĂ©brique, gĂ©nĂ©ralitĂ©s, groupes commutatifs, Masson & Cie, Éditeurs, Paris; North-Holland Publishing Co., Amsterdam, 1970 (French). Avec un appendice Corps de classes local par Michiel Hazewinkel. MR 0302656
  • Jean Giraud, Cohomologie non abĂ©lienne, Die Grundlehren der mathematischen Wissenschaften, Band 179, Springer-Verlag, Berlin-New York, 1971 (French). MR 0344253
  • [EGA]EGA A. Grothendieck, ÉlĂ©ments de GĂ©omĂ©trie AlgĂ©brique, III, Publ. Math. IHES 24.
  • Maxim Kontsevich, Deformation quantization of algebraic varieties, Lett. Math. Phys. 56 (2001), no. 3, 271–294. EuroConfĂ©rence MoshĂ© Flato 2000, Part III (Dijon). MR 1855264, DOI 10.1023/A:1017957408559
  • James S. Milne, Étale cohomology, Princeton Mathematical Series, No. 33, Princeton University Press, Princeton, N.J., 1980. MR 559531
  • Ryszard Nest and Boris Tsygan, Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems, Asian J. Math. 5 (2001), no. 4, 599–635. MR 1913813, DOI 10.4310/AJM.2001.v5.n4.a2
  • Amnon Yekutieli, Deformation quantization in algebraic geometry, Adv. Math. 198 (2005), no. 1, 383–432. MR 2183259, DOI 10.1016/j.aim.2005.06.009
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Additional Information
  • R. Bezrukavnikov
  • Affiliation: Department of Mathematics, Massachusets Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 347192
  • Email: bezrukav@math.mit.edu
  • 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.
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 21 (2008), 409-438
  • MSC (2000): Primary 14M99
  • DOI: https://doi.org/10.1090/S0894-0347-07-00585-1
  • MathSciNet review: 2373355