Title: Deformation Quantization in Algebraic Geometry
Authors: Amnon Yekutieli
Publication status: Advances in Mathematics 198 (2005), 383-432 (Michael Artin Volume).
Erratum: Advances in Mathematics 217 (2008), 2897-2906
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.
Electronic version of paper:
pdf file (acrobat)
journal pdf file
* journal pdf file (prepublication)
* Lemma 3.5 in the paper is most likely wrong, and consequently Corollary 3.10 has no proof. This is corrected in Theorem 0.4 the paper "MC Elements in Pronilpotent DG Lie Algebras".
28 December 2014)