{
  "id": "math/0609716",
  "version": "v1",
  "published": "2006-09-26T01:12:57.000Z",
  "updated": "2006-09-26T01:12:57.000Z",
  "title": "Jacobi sums, Fermat Jacobians, and ranks of abelian varieties over towers of function fields",
  "authors": [
    "Douglas Ulmer"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "Our goal in this note is to give a number of examples of abelian varieties over function fields k(t) which have bounded ranks in towers of extensions such as k(t^{1/d}) for varying d. Along the way we prove some new results on Fermat curves which may be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-09-26T01:12:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G05",
      "11G40"
    ],
    "keywords": [
      "abelian varieties",
      "function fields",
      "fermat jacobians",
      "jacobi sums",
      "fermat curves"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9716U"
    }
  }
}