{
  "id": "0712.3987",
  "version": "v4",
  "published": "2007-12-24T11:01:51.000Z",
  "updated": "2009-09-01T12:29:07.000Z",
  "title": "Functional equations of the dilogarithm in motivic cohomology",
  "authors": [
    "Oliver Petras"
  ],
  "comment": "21 pages, no figures; accepted for publication in the Journal of Number Theory",
  "journal": "Journal of Number Theory 129 (2009) pp. 2346-2368",
  "doi": "10.1016/j.jnt.2009.04.009",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove relations between fractional linear cycles in Bloch's integral cubical higher Chow complex in codimension two of number fields, which correspond to functional equations of the dilogarithm. These relations suffice, as we shall demonstrate with a few examples, to write down enough relations in Bloch's integral higher Chow group CH^2(F,3) for certain number fields F to detect torsion cycles. Using the regulator map to Deligne cohomology, one can check the non-triviality of the torsion cycles thus obtained. Using this combination of methods, we obtain explicit higher Chow cycles generating the integral motivic cohomology groups of some number fields.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2009-09-01T12:29:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G55",
      "11R70",
      "11S70",
      "11F42"
    ],
    "keywords": [
      "functional equations",
      "motivic cohomology",
      "cubical higher chow complex",
      "integral cubical higher chow",
      "number fields"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0712.3987P"
    }
  }
}