{
  "id": "math/0606422",
  "version": "v2",
  "published": "2006-06-19T14:38:02.000Z",
  "updated": "2006-10-16T10:04:01.000Z",
  "title": "Abelian varieties without homotheties",
  "authors": [
    "Yuri G. Zarhin"
  ],
  "comment": "8 pages",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "A celebrated theorem of Bogomolov asserts that the $\\ell$-adic Lie algebra attached to the Galois action on the Tate module of an abelian variety over a number field contains all homotheties. This is not the case in characteristic $p$: a \"counterexample\" is provided by an ordinary elliptic curve defined over a finite field. In this note we discuss (and explicitly construct) more interesting examples of \"non-constant\" absolutely simple abelian varieties (without homotheties) over global fields in characteristic $p$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-10-16T10:04:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "14G25"
    ],
    "keywords": [
      "abelian variety",
      "homotheties",
      "absolutely simple abelian varieties",
      "number field contains",
      "adic lie algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6422Z"
    }
  }
}