**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

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.**Electronic
version of paper:**pdf
file (acrobat)

journal pdf file

**Errata:***
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)