{
  "id": "math/9908019",
  "version": "v1",
  "published": "1999-08-05T05:13:29.000Z",
  "updated": "1999-08-05T05:13:29.000Z",
  "title": "Arithmetic Hodge structure and higher Abel-Jacobi maps",
  "authors": [
    "Masanori Asakura"
  ],
  "comment": "Latex2e, 20pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "In this paper, we show some applications to algebraic cycles by using higher Abel-Jacobi maps which were defined in [the author: Motives and algebraic de Rham cohomology]. In particular, we prove that the Beilinson conjecture on algebraic cycles over number fields implies the Bloch conjecture on zero-cycles on surfaces. Moreover, we construct a zero-cycle on a product of curves whose Mumford invariant vanishes, but not higher Abel-Jacobi invariant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-08-05T05:13:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C30",
      "32S35"
    ],
    "keywords": [
      "higher abel-jacobi maps",
      "arithmetic hodge structure",
      "algebraic cycles",
      "mumford invariant vanishes",
      "higher abel-jacobi invariant"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......8019A"
    }
  }
}