{
  "id": "2001.01104",
  "version": "v1",
  "published": "2020-01-04T17:52:20.000Z",
  "updated": "2020-01-04T17:52:20.000Z",
  "title": "Cyclicity of some families of isogeny classes of abelian varieties over finite fields",
  "authors": [
    "Alejandro J. Giangreco-Maidana"
  ],
  "comment": "8 pages, comments are welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "An isogeny class $\\mathcal{A}$ of abelian varieties defined over finite fields is said to be \"cyclic\" if every variety in $\\mathcal{A}$ has a cyclic group of rational points. In these notes we study the cyclicity of isogeny classes of abelian varieties with Weil polynomials of the form $f_\\mathcal{A}(t)=t^{2g}+at^g+q^g$. We exploit the criterion: an isogeny class $\\mathcal{A}$ with Weil polynomial $f$ is cyclic if and only if $\\widehat{f(1)}$ is coprime with $f'(1)$, where $\\widehat{f(1)}$ is the ratio of $f(1)$ to its radical.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-04T17:52:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "14G15",
      "14K15"
    ],
    "keywords": [
      "isogeny class",
      "abelian varieties",
      "finite fields",
      "weil polynomial",
      "cyclic group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}