Deformation Quantization in Algebraic Geometry
Abstract
We study deformation quantizations of the structure sheaf OX of a smooth algebraic variety X in characteristic 0. Our main result is that when X is D-affine, any formal Poisson structure on X determines a deformation quantization of OX (canonically, up to gauge equivalence). This is an algebro-geometric analogue of Kontsevich's celebrated result.
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