{
  "id": "1512.02026",
  "version": "v1",
  "published": "2015-12-07T13:00:46.000Z",
  "updated": "2015-12-07T13:00:46.000Z",
  "title": "A higher dimensional generalization of Lichtenbaum duality in terms of the Albanese map",
  "authors": [
    "Wataru Kai"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We present a conjectural formula describing the cokernel of the Albanese map of zero-cycles of smooth projective varieties $X$ over $p$-adic fields in terms of the N\\'eron-Severi group and provide a proof under additional assumptions on an integral model of $X$. The proof depends on a non-degeneracy result of Brauer-Manin pairing due to Saito-Sato and on Gabber-de Jong's comparison result of cohomological- and Azumaya-Brauer groups. We can consider the local-global problem of the Albanese-cokernel; the abelian group on the \"local side\" turns out to be a finite group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-12-07T13:00:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "higher dimensional generalization",
      "albanese map",
      "lichtenbaum duality",
      "gabber-de jongs comparison result",
      "azumaya-brauer groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}