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".

(updated  28 December 2014)