{
  "id": "math/0110180",
  "version": "v2",
  "published": "2001-10-17T15:10:46.000Z",
  "updated": "2001-11-08T05:37:34.000Z",
  "title": "An analogue of cyclotomic units for products of elliptic curves",
  "authors": [
    "Srinath Baba",
    "Ramesh Sreekantan"
  ],
  "comment": "25 pages. Typos and a statement of a theorem of Scholl and Harris corrected",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We construct certain elements in the integral motivic cohomology group $H^3_{{\\cal M}}(E \\times E',\\Q(2))_{\\ZZ}$, where $E$ and $E'$ are elliptic curves over $\\Q$. When $E$ is not isogenous to $E'$ these elements are analogous to `cyclotomic units' in real quadratic fields as they come from modular parametrisations of the elliptic curves. We then find an analogue of the class number formula for real quadratic fields. Finally we use the Beilinson conjectures for $E \\times E'$ to deduce them for products of $n$ elliptic curves. A certain amount of this paper is expository in nature.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2001-11-08T05:37:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G16",
      "11G18",
      "14C25"
    ],
    "keywords": [
      "elliptic curves",
      "cyclotomic units",
      "real quadratic fields",
      "integral motivic cohomology group",
      "class number formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001math.....10180B"
    }
  }
}