{
  "id": "math/9803039",
  "version": "v1",
  "published": "1998-03-11T15:56:33.000Z",
  "updated": "1998-03-11T15:56:33.000Z",
  "title": "Germs of arcs on singular algebraic varieties and motivic integration",
  "authors": [
    "J. Denef",
    "F. Loeser"
  ],
  "comment": "Revised Nov. 1997, to appear in Inventiones Mathematicae, 27 pages",
  "journal": "Invent. Math. 135 (1999), no. 1, 201--232",
  "doi": "10.1007/s002220050284",
  "categories": [
    "math.AG"
  ],
  "abstract": "We study the scheme of formal arcs on a singular algebraic variety and its images under truncations. We prove a rationality result for the Poincare series of these images which is an analogue of the rationality of the Poincare series associated to p-adic points on a p-adic variety. The main tools which are used are semi-algebraic geometry in spaces of power series and motivic integration (a notion introduced by M. Kontsevich). In particular we develop the theory of motivic integration for semi-algebraic sets of formal arcs on singular algebraic varieties, we prove a change of variable formula for birational morphisms and we prove a geometric analogue of a result of Oesterle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-03-11T15:56:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A15",
      "14B05",
      "32S05",
      "32S45",
      "03C10"
    ],
    "keywords": [
      "singular algebraic variety",
      "motivic integration",
      "poincare series",
      "formal arcs",
      "semi-algebraic sets"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}