{
  "id": "math/0310399",
  "version": "v5",
  "published": "2003-10-24T23:45:09.000Z",
  "updated": "2005-07-09T19:43:59.000Z",
  "title": "Deformation Quantization in Algebraic Geometry",
  "authors": [
    "Amnon Yekutieli"
  ],
  "comment": "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 version",
  "categories": [
    "math.AG",
    "math.QA",
    "math.RA"
  ],
  "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.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2005-07-09T19:43:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53D55",
      "14D15",
      "13D10",
      "16S80"
    ],
    "keywords": [
      "algebraic geometry",
      "study deformation quantizations",
      "smooth algebraic variety",
      "formal poisson structure",
      "main result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....10399Y"
    }
  }
}