{
  "id": "math/0002009",
  "version": "v2",
  "published": "2000-02-01T12:55:28.000Z",
  "updated": "2000-02-07T12:25:53.000Z",
  "title": "Bloch's Conjecture and Chow Motives",
  "authors": [
    "Morihiko Saito"
  ],
  "comment": "AMS-TeX, 7 pages; minor change",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let X be a complex surface with no nontrivial 2-forms. Then we show that Bloch's conjecture is true (i.e. the Albanese map in this case is injective) if and only if any homologically trivial idempotent in the ring of correspondences vanishes. Furthermore the cube of the ideal of homologically trivial correspondences is zero if these equivalent conditions are satisfied (e.g. if X is not of general type).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2000-02-07T12:25:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C30",
      "32S35"
    ],
    "keywords": [
      "blochs conjecture",
      "chow motives",
      "complex surface",
      "equivalent conditions",
      "homologically trivial correspondences"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......2009S"
    }
  }
}