{
  "id": "math/0611606",
  "version": "v1",
  "published": "2006-11-20T13:39:01.000Z",
  "updated": "2006-11-20T13:39:01.000Z",
  "title": "Explicit n-descent on elliptic curves, II. Geometry",
  "authors": [
    "John Cremona",
    "Tom Fisher",
    "Cathy O'Neil",
    "Denis Simon",
    "Michael Stoll"
  ],
  "comment": "24 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "This is the second in a series of papers in which we study the n-Selmer group of an elliptic curve. In this paper, we show how to realize elements of the n-Selmer group explicitly as curves of degree n embedded in P^{n-1}. The main tool we use is a comparison between an easily obtained embedding into P^{n^2-1} and another map into P^{n^2-1} that factors through the Segre embedding P^{n-1} x P^{n-1} --> P^{n^2-1}. The comparison relies on an explicit version of the local-to-global principle for the n-torsion of the Brauer group of the base field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-11-20T13:39:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G05",
      "14H52",
      "14H25"
    ],
    "keywords": [
      "elliptic curve",
      "explicit n-descent",
      "main tool",
      "base field",
      "brauer group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....11606C"
    }
  }
}