{
  "id": "2101.12664",
  "version": "v1",
  "published": "2021-01-29T16:11:57.000Z",
  "updated": "2021-01-29T16:11:57.000Z",
  "title": "Maximal abelian varieties over finite fields and cyclicity",
  "authors": [
    "Elena Berardini",
    "Alejandro J. Giangreco Maidana"
  ],
  "comment": "10 pages, comments are welcome",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Let $\\mathcal{M}_g^0(q)$ denote the isogeny class (if it is unique) of $g$-dimensional abelian varieties defined over $\\mathbb{F}_q$ with maximal number of rational points among those with endomorphism algebra being a field. We describe a polynomial $h_g(t,X)$ such that for every even power $q$ of a prime and verifying mild conditions, $h_g(t,\\sqrt{q})$ is the Weil polynomial of $\\mathcal{M}_g^0(q)$. It turns out that in this case, $\\mathcal{M}_g^0(q)$ is ordinary and cyclic outside the primes dividing an integer $N_g$ that only depends on $g$. We also give explicitly $h_3(t,X)$ and prove that $\\mathcal{M}_3^0(q)$ is ordinary and cyclic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-29T16:11:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "14G05",
      "14G15",
      "14K02"
    ],
    "keywords": [
      "maximal abelian varieties",
      "finite fields",
      "dimensional abelian varieties",
      "maximal number",
      "isogeny class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}