Deformation Quantization in Algebraic Geometry

Details Deformation Quantization in Algebraic Geometry Deformation Quantization in Algebraic Geometry

2003-10-24

arxiv.org/abs/math/0310399v5

Mathematics

Algebraic Geometry

AMSLaTeX, 41 pages, XYpic and eps figures. Final version; to appear in Advances Math (Michael Artin issue). Several new techni

Scientific paper

We study deformation quantizations of the structure sheaf O_X 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 O_X (canonically, up to gauge equivalence). This is an
algebro-geometric analogue of Kontsevich's celebrated result.

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