{
  "id": "1501.02446",
  "version": "v1",
  "published": "2015-01-11T11:24:10.000Z",
  "updated": "2015-01-11T11:24:10.000Z",
  "title": "Categories of abelian varieties over finite fields I. Abelian varieties over $\\mathbb{F}_p$",
  "authors": [
    "Tommaso Giorgio Centeleghe",
    "Jakob Stix"
  ],
  "comment": "Accepted for publication in Algebra & Number Theory",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We assign functorially a $\\mathbb{Z}$-lattice with semisimple Frobenius action to each abelian variety over $\\mathbb{F}_p$. This establishes an equivalence of categories that describes abelian varieties over $\\mathbb{F}_p$ avoiding $\\sqrt{p}$ as an eigenvalue of Frobenius in terms of simple commutative algebra. The result extends the isomorphism classification of Waterhouse and Deligne's equivalence for ordinary abelian varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-11T11:24:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "14K10"
    ],
    "keywords": [
      "abelian variety",
      "finite fields",
      "categories",
      "ordinary abelian varieties",
      "semisimple frobenius action"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}