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arXiv:math/0310399 [math.AG]AbstractReferencesReviewsResources

Deformation Quantization in Algebraic Geometry

Amnon Yekutieli

Published 2003-10-24, updated 2005-07-09Version 5

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.

Comments: AMSLaTeX, 41 pages, XYpic and eps figures. Final version; to appear in Advances Math (Michael Artin issue). Several new technical results and remarks in this version
Categories: math.AG, math.QA, math.RA
Subjects: 53D55, 14D15, 13D10, 16S80
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