{
  "id": "math/0607272",
  "version": "v1",
  "published": "2006-07-12T00:57:47.000Z",
  "updated": "2006-07-12T00:57:47.000Z",
  "title": "Algebraic cycles and Connes periodicity",
  "authors": [
    "Jinhyun Park"
  ],
  "comment": "25 pages",
  "categories": [
    "math.AG",
    "math.KT"
  ],
  "abstract": "We apply the classical technique on cyclic objects of Alain Connes to various objects, in particular to the higher Chow complex of S. Bloch to prove a Connes periodicity long exact sequence involving motivic cohomology groups. The Cyclic higher Chow groups and the Connes higher Chow groups of a variety are defined in the process and various properties of them are deduced from the known properties of the higher Chow groups. Applications include an equivalent reformulation of the Beilinson-Soul\\'e vanishing conjecture for the motivic cohomology groups of a smooth variety $X$ and a reformulation of the conjecture of Soul\\'e on the order of vanishing of the zeta function of an arithmetic variety.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-12T00:57:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C25",
      "19D55"
    ],
    "keywords": [
      "algebraic cycles",
      "motivic cohomology groups",
      "connes periodicity long exact sequence",
      "cyclic higher chow groups",
      "connes higher chow groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7272P"
    }
  }
}