{
  "id": "1311.5454",
  "version": "v1",
  "published": "2013-11-21T15:45:01.000Z",
  "updated": "2013-11-21T15:45:01.000Z",
  "title": "A Deuring criterion for abelian varieties",
  "authors": [
    "Chris Blake"
  ],
  "comment": "7 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give several generalisations of the Deuring reduction criterion for elliptic curves to abelian varieties of higher dimension. In particular the Newton polygon of the reduction of an abelian variety A with complex multiplication by F at a prime above p can be explicitly computed in terms of the CM type of A and the decomposition group of a suitable prime above p in a Galois closure of F. Conversely, it is shown that the formal isogeny type of the reduction of A at a prime above p places certain restrictions on the decomposition of p in F.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-11-21T15:45:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "11G15"
    ],
    "keywords": [
      "abelian variety",
      "deuring criterion",
      "formal isogeny type",
      "elliptic curves",
      "galois closure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1311.5454B"
    }
  }
}