Fedosov quantization in positive characteristic

Details Fedosov quantization in positive characteristic Fedosov quantization in positive characteristic

2005-01-16

arxiv.org/abs/math/0501247v3

Mathematics

Algebraic Geometry

39 pages, LaTeX2e. Final version, to appear in JAMS

Scientific paper

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 restrictted Lie algebra -- and we prove a version of Darboux Theorem valid in positive characteristic setting.

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