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", Eprint arXiv:1103.1035
at
http://arxiv.org.
updated
16 Mar 2010