Deformation quantization in algebraic geometry
-- Amnon Yekutieli

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We study deformation
quantization of the structure sheaf O_X of a smooth algebraic variety X in
characteristic 0. The method used is the universal deformation formula of
Kontsevich, plus an algebro-geometric treatment of the bundle of formal
coordinate systems of X. If X is a D-affine variety (e.g. P^n or more generally
a flag variety) we obtain a canonical quantization map from the set of gauge
equivalence classes of formal Poisson structures on X to the set of gauge
equivalence classes of deformation quantizations of O_X. This is an
algebro-geometric analogue of Kontsevich's celebrated result.