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Deformation Quantization in Algebraic Geometry

Amnon Yekutieli
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Abstract

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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Amnon Yekutieli. 2005-07-09. Deformation Quantization in Algebraic Geometry. https://arxiv.org/abs/math/0310399

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