Deformation Quantization in Algebraic Geometry
代数几何
2007-05-23 v5 量子代数
环与代数
摘要
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.
引用
@article{arxiv.math/0310399,
title = {Deformation Quantization in Algebraic Geometry},
author = {Amnon Yekutieli},
journal= {arXiv preprint arXiv:math/0310399},
year = {2007}
}
备注
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