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)