{
  "id": "2002.02067",
  "version": "v1",
  "published": "2020-02-06T02:02:13.000Z",
  "updated": "2020-02-06T02:02:13.000Z",
  "title": "Restrictions on Weil polynomials of Jacobians of hyperelliptic curves",
  "authors": [
    "Edgar Costa",
    "Ravi Donepudi",
    "Ravi Fernando",
    "Valentijn Karemaker",
    "Caleb Springer",
    "Mckenzie West"
  ],
  "comment": "15 pages, 1 figure",
  "categories": [
    "math.NT"
  ],
  "abstract": "Inspired by experimental data, this paper investigates which isogeny classes of abelian varieties defined over a finite field of odd characteristic contain the Jacobian of a hyperelliptic curve. We provide a necessary condition by demonstrating that the Weil polynomial of a hyperelliptic Jacobian must have a particular form modulo 2. For fixed ${g\\geq1}$, the proportion of isogeny classes of $g$ dimensional abelian varieties defined over $\\mathbb{F}_q$ which fail this condition is $1 - Q(2g + 2)/2^g$ as $q\\to\\infty$ ranges over odd prime powers, where $Q(n)$ denotes the number of partitions of $n$ into odd parts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-06T02:02:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G20",
      "11M38"
    ],
    "keywords": [
      "hyperelliptic curve",
      "weil polynomial",
      "restrictions",
      "isogeny classes",
      "odd characteristic contain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}