{
  "id": "math/0101050",
  "version": "v1",
  "published": "2001-01-06T20:52:12.000Z",
  "updated": "2001-01-06T20:52:12.000Z",
  "title": "Hyperelliptic jacobians without complex multiplication in positive characteristic",
  "authors": [
    "Yuri G. Zarhin"
  ],
  "comment": "LaTeX2e, 6 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We prove that in odd characteristic the jacobian of a hyperelliptic curve $y^2=f(x)$ has no nontrivial endomorphisms over an algebraic closure of the ground field if the Galois group of the polynomial $f$ of even degree is ``very big\". The case of characteristic zero was previously treated by the author (Math. Res. Letters 7(2000), 123--132).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-01-06T20:52:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H40",
      "14K05",
      "11G30",
      "11G10"
    ],
    "keywords": [
      "complex multiplication",
      "hyperelliptic jacobians",
      "positive characteristic",
      "characteristic zero",
      "odd characteristic"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math......1050Z"
    }
  }
}