{
  "id": "1203.2650",
  "version": "v2",
  "published": "2012-03-12T21:03:30.000Z",
  "updated": "2013-09-24T15:39:50.000Z",
  "title": "Algebraic cycles and fibrations",
  "authors": [
    "Charles Vial"
  ],
  "comment": "Supersedes arXiv:1203.2650",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $f : X -> B$ be a projective surjective morphism between quasi-projective varieties. The goal of this paper is the study of the Chow groups of $X$ in terms of the Chow groups of $B$ and of the fibers of $f$. One of the applications concerns quadric bundles. When $X$ and $B$ are smooth projective and when $f$ is a flat quadric fibration, we show that the motive of $X$ is \"built\" from the motives of varieties of dimension less than the dimension of $B$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-09-24T15:39:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C15",
      "14C25",
      "14C05",
      "14D99"
    ],
    "keywords": [
      "algebraic cycles",
      "chow groups",
      "applications concerns quadric bundles",
      "flat quadric fibration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.2650V"
    }
  }
}