{
  "id": "0709.1979",
  "version": "v4",
  "published": "2007-09-13T02:53:42.000Z",
  "updated": "2008-05-01T18:53:52.000Z",
  "title": "K3 surfaces of finite height over finite fields",
  "authors": [
    "J. -D. Yu",
    "N. Yui"
  ],
  "comment": "Cor.3.4 added, typos corrected, to appear in J. Math. Kyoto Univ",
  "categories": [
    "math.AG"
  ],
  "abstract": "Arithmetic of K3 surfaces defined over finite fields is investigated. In particular, we show that any K3 surface of finite height over a finite field k of characteristic p > 3 has a quasi-canonical lifting to characteristic 0, and that for any such lifting, the endormorphism algebra of the transcendental cycles, as a Hodge module, is a CM field. The Tate conjecture for the product of certain two K3 surfaces is also proved. We illustrate by examples how to determine explicitly the formal Brauer group associated to a K3 surface over k. Examples discussed here are all of hypergeometric type.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2008-05-01T18:53:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J28",
      "14G15"
    ],
    "keywords": [
      "finite field",
      "finite height",
      "transcendental cycles",
      "hypergeometric type",
      "characteristic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.1979Y"
    }
  }
}