Geodesic
Fedosov quantization in positive characteristic
Bezrukavnikov, R.1 ; Kaledin, D.2
1 Department of Mathematics, Massachusets Institute of Technology, Cambridge, Massachusetts 02139
2 Steklov Institute, Gubkina 8, Moscow, 119991, Russia
Journal of the American Mathematical Society, Tome 21 (2008) no. 2, pp. 409-438

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-07-00585-1

Bezrukavnikov, R. 1 ; Kaledin, D. 2

1 Department of Mathematics, Massachusets Institute of Technology, Cambridge, Massachusetts 02139
2 Steklov Institute, Gubkina 8, Moscow, 119991, Russia 
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Bezrukavnikov, R.; Kaledin, D. Fedosov quantization in positive characteristic. Journal of the American Mathematical Society, Tome 21 (2008) no. 2, pp. 409-438. doi: 10.1090/S0894-0347-07-00585-1

[1] Bezrukavnikov, R., Kaledin, D. Fedosov quantization in algebraic context Mosc. Math. J. 2004

[2] Bezrukavnikov, R. V., Kaledin, D. B. McKay equivalence for symplectic resolutions of quotient singularities Tr. Mat. Inst. Steklova 2004 20 42

[3] Demazure, Michel Lectures on 𝑝-divisible groups 1972

[4] Demazure, Michel, Gabriel, Pierre Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs 1970

[5] Giraud, Jean Cohomologie non abélienne 1971

[6] Kontsevich, Maxim Deformation quantization of algebraic varieties Lett. Math. Phys. 2001 271 294

[7] Milne, James S. Étale cohomology 1980

[8] Nest, Ryszard, Tsygan, Boris Deformations of symplectic Lie algebroids, deformations of holomorphic symplectic structures, and index theorems Asian J. Math. 2001 599 635

[9] Yekutieli, Amnon Deformation quantization in algebraic geometry Adv. Math. 2005 383 432

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