{
  "id": "1803.09291",
  "version": "v4",
  "published": "2018-03-25T16:34:52.000Z",
  "updated": "2019-01-02T06:21:59.000Z",
  "title": "Duality for cohomology of curves with coefficients in abelian varieties",
  "authors": [
    "Takashi Suzuki"
  ],
  "comment": "79 pages. Accepted for publication in Nagoya Mathematical Journal",
  "doi": "10.1017/nmj.2018.46",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "In this paper, we formulate and prove a duality for cohomology of curves over perfect fields of positive characteristic with coefficients in Neron models of abelian varieties. This is a global function field version of the author's previous work on local duality and Grothendieck's duality conjecture. It generalizes the perfectness of the Cassels-Tate pairing in the finite base field case. The proof uses the local duality mentioned above, Artin-Milne's global finite flat duality, the non-degeneracy of the height pairing and finiteness of crystalline cohomology. All these ingredients are organized under the formalism of the rational etale site developed earlier.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2019-01-02T06:21:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11R58",
      "14F20"
    ],
    "keywords": [
      "abelian varieties",
      "cohomology",
      "artin-milnes global finite flat duality",
      "coefficients",
      "rational etale site developed earlier"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 79,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}