{
  "id": "math/9910113",
  "version": "v14",
  "published": "1999-10-21T15:34:48.000Z",
  "updated": "2002-11-18T11:52:18.000Z",
  "title": "Bloch's Conjecture, Deligne Cohomology and Higher Chow Groups",
  "authors": [
    "Morihiko Saito"
  ],
  "comment": "33 pages, the bijectivity of the Albanese map is treated in (0.4), and a weak Lefschetz-type theorem for (higher) Chow groups is studied",
  "categories": [
    "math.AG"
  ],
  "abstract": "We express the kernel of Griffiths' Abel-Jacobi map by using the inductive limit of Deligne cohomology in the generalized sense (i.e. the absolute Hodge cohomology of A. Beilinson). This generalizes a result of L. Barbieri-Viale and V. Srinivas in the surface case. We then show that the Abel-Jacobi map for codimension 2 cycles and the Albanese map are bijective if a general hyperplane section is a surface for which Bloch's conjecture is proved. In certain cases we verify Nori's conjecture on the Griffiths group. We also prove a weak Lefschetz-type theorem for (higher) Chow groups, generalize a formula for the Abel-Jacobi map of higher cycles due to Beilinson and Levine to the smooth non proper case, and give a sufficient condition for the nonvanishing of the transcendental part of the image by the Abel-Jacobi map of a higher cycle on an elliptic surface, together with some examples.",
  "revisions": [
    {
      "version": "v14",
      "updated": "2002-11-18T11:52:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C30",
      "32S35"
    ],
    "keywords": [
      "higher chow groups",
      "deligne cohomology",
      "blochs conjecture",
      "abel-jacobi map",
      "higher cycle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....10113S"
    }
  }
}