{
  "id": "2103.16530",
  "version": "v1",
  "published": "2021-03-30T17:34:03.000Z",
  "updated": "2021-03-30T17:34:03.000Z",
  "title": "Every positive integer is the order of an ordinary abelian variety over ${\\mathbb F}_2$",
  "authors": [
    "Everett W. Howe",
    "Kiran S. Kedlaya"
  ],
  "comment": "5 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We show that for every integer $m > 0$, there is an ordinary abelian variety over ${\\mathbb F}_2$ that has exactly $m$ rational points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-30T17:34:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A67",
      "11G10",
      "14G15",
      "14K15"
    ],
    "keywords": [
      "ordinary abelian variety",
      "positive integer",
      "rational points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}