{
  "id": "2002.04420",
  "version": "v1",
  "published": "2020-02-11T14:40:40.000Z",
  "updated": "2020-02-11T14:40:40.000Z",
  "title": "On the lower bound of the number of abelian varieties over $\\mathbb{F}_p$",
  "authors": [
    "Jungin Lee"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we prove that the number $B(p,g)$ of isomorphism classes of abelian varieties over a prime field $\\mathbb{F}_p$ of dimension $g$ has a lower bound $\\left( \\frac{e}{4} \\right)^{\\frac{1}{4} g^2} p^{\\frac{1}{2} g^2 (1+o(1))}$ as $g \\rightarrow \\infty$. This is the first nontrivial result on the lower bound of $B(p,g)$. We also improve the upper bound $2^{34g^2} p^{\\frac{69}{4} g^2 (1+o(1))}$ of $B(p,g)$ given by Lipnowski and Tsimerman (Duke Math. 167:3403-3453, 2018) to $p^{\\frac{45}{4} g^2(1+o(1))}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-11T14:40:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G25"
    ],
    "keywords": [
      "lower bound",
      "abelian varieties",
      "first nontrivial result",
      "isomorphism classes",
      "duke math"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}