{
  "id": "math/0410024",
  "version": "v1",
  "published": "2004-10-01T17:02:41.000Z",
  "updated": "2004-10-01T17:02:41.000Z",
  "title": "Hodge structures on abelian varieties of type III",
  "authors": [
    "Salman Abdulali"
  ],
  "comment": "14 pages, published version",
  "journal": "Annals of Math. (2), Vol. 155 (2002), no. 3, 915--928",
  "categories": [
    "math.AG",
    "math.GR"
  ],
  "abstract": "We show that the usual Hodge conjecture implies the general Hodge conjecture for certain abelian varieties of type III, and use this to deduce the general Hodge conjecture for all powers of certain 4-dimensional abelian varieties of type III. We also show the existence of a Hodge structure M such that M occurs in the cohomology of an abelian variety, but the Tate twist M(1) does not occur in the cohomology of any abelian variety, even though it is effective.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-10-01T17:02:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14C30",
      "14K20",
      "20G30"
    ],
    "keywords": [
      "abelian variety",
      "hodge structure",
      "general hodge conjecture",
      "usual hodge conjecture implies",
      "tate twist"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....10024A"
    }
  }
}