2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68979We 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.AMSLaTeX, 41 pages, XYpic and eps figures. Final version; to appear in Advances Math (Michael Artin issue). Several new technical results and remarks in this versionAlgebraic GeometryQuantum AlgebraRings and Algebras(Classification 2000) Primary: 53D55; Secondary: 14D15, 13D10, 16S80text