{
  "id": "1806.00368",
  "version": "v1",
  "published": "2018-06-01T14:24:28.000Z",
  "updated": "2018-06-01T14:24:28.000Z",
  "title": "Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in $p$-adic cohomology",
  "authors": [
    "Edgar Costa",
    "David Harvey",
    "Kiran S. Kedlay"
  ],
  "comment": "17 pages, 3 figures",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We give an interim report on some improvements and generalizations of the Abbott--Kedlaya--Roe method to compute the zeta function of a nondegenerate ample hypersurface in a projectively normal toric variety over $\\mathbb{F}_p$ in linear time in $p$. These are illustrated with a number of examples including K3 surfaces, Calabi--Yau threefolds, and a cubic fourfold. The latter example is a non-special cubic fourfold appearing in the Ranestad--Voisin coplanar divisor on moduli space; this verifies that the coplanar divisor is not a Noether--Lefschetz divisor in the sense of Hassett.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-06-01T14:24:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G25",
      "14G10",
      "11M38",
      "11Y16",
      "14C25"
    ],
    "keywords": [
      "zeta function",
      "adic cohomology",
      "nondegenerate hypersurfaces",
      "controlled reduction",
      "nondegenerate ample hypersurface"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}