{
  "id": "math/0111073",
  "version": "v1",
  "published": "2001-11-07T09:48:42.000Z",
  "updated": "2001-11-07T09:48:42.000Z",
  "title": "Theoreme de Van Kampen pour les champs algebriques",
  "authors": [
    "V. Zoonekynd"
  ],
  "comment": "latex2e with xypic, 42 pages, 1 figure, in French",
  "categories": [
    "math.AG",
    "math.CT"
  ],
  "abstract": "We define a category whose objects are finite etale coverings of an algebraic stack and prove that it is a Galois category and that it allows one to compute the fundamental group of the stack. We then prove a Van Kampen theorem for algebraic stacks whose simplest form reads: Let U and V be open substacks of an algebraic stack X with X = U \\union V, let P be a set of base points, at least one in each connected component of X, U, V and U \\inter V, then pi_1(X,P) is the amalgamated sum of pi_1(U,P) and pi_1(V,P) over pi_1(U \\inter V, P).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-11-07T09:48:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14F35",
      "14A20",
      "18B25",
      "20L05",
      "18D05"
    ],
    "keywords": [
      "van kampen pour",
      "champs algebriques",
      "algebraic stack",
      "simplest form reads",
      "finite etale coverings"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 42,
      "language": "fr",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....11073Z"
    }
  }
}