{
  "id": "1203.2651",
  "version": "v1",
  "published": "2012-03-12T21:03:41.000Z",
  "updated": "2012-03-12T21:03:41.000Z",
  "title": "Chow groups of smooth varieties fibred by quadrics",
  "authors": [
    "Charles Vial"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $f : X \\rightarrow B$ be a proper flat dominant morphism between two smooth quasi-projective complex varieties $X$ and $B$. Assume that there exists an integer $l$ such that all closed fibres $X_b$ of $f$ satisfy $CH_j(X_b) = \\Q$ for all $j \\leq l$. Then we prove an analogue of the projective bundle formula for $CH_i(X)$ for $i \\leq l$. When $B$ is a surface, $X$ is projective and $l = \\lfloor \\frac{\\dim X - 3}{2} \\rfloor$, this makes it possible to construct a Chow-K\\\"unneth decomposition for $X$ that satisfies Murre's conjectures. For instance we prove Murre's conjectures for complex smooth projective varieties $X$ fibred over a surface (via a flat morphism) by quadrics, or by complete intersections of dimension 4 of bidegree $(2,2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-03-12T21:03:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25",
      "14C15"
    ],
    "keywords": [
      "smooth varieties",
      "chow groups",
      "proper flat dominant morphism",
      "smooth quasi-projective complex varieties",
      "satisfies murres conjectures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.2651V"
    }
  }
}