{
  "id": "math/0507475",
  "version": "v1",
  "published": "2005-07-22T13:16:27.000Z",
  "updated": "2005-07-22T13:16:27.000Z",
  "title": "Modifications et cycles évanescents sur une base de dimension supérieure à un",
  "authors": [
    "Fabrice Orgogozo"
  ],
  "comment": "In French. Submitted to IMRN",
  "journal": "International Mathematics Research Notices 2006 (2006) Article ID 25315, 38 pages",
  "doi": "10.1155/IMRN/2006/25315",
  "categories": [
    "math.AG"
  ],
  "abstract": "For a given morphism of schemes f:X->S, a sheaf F on X, a geometric point x on X, and s=f(x), the morphism f\\_x : X(x) -> S(s) between the strict henselizations doesn't necessarily behave (with respect to F) like a proper morphism. However, we know it is so (assuming constructibility of F etc.) if S is the spectrum of a dvr (P. Deligne, SGA 4 1/2, [Th. finitude]). In this article, we prove it becomes so after an appropriate modification of the base S. The main ingredient is a theorem by A.J. de Jong on plurinodal fibrations. An application of this formalism to Lefschetz pencils is given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-22T13:16:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dimension supérieure",
      "proper morphism",
      "geometric point",
      "appropriate modification",
      "lefschetz pencils"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "fr",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7475O"
    }
  }
}