{
  "id": "math/0208118",
  "version": "v1",
  "published": "2002-08-14T22:18:51.000Z",
  "updated": "2002-08-14T22:18:51.000Z",
  "title": "Kummer theory of abelian varieties and reductions of Mordell-Weil groups",
  "authors": [
    "Tom Weston"
  ],
  "categories": [
    "math.NT",
    "math.AC"
  ],
  "abstract": "Let A be an abelian variety over a number field F with End(A/F) commutative. Let S be a subgroup of A(F) and let x be a point of A(F). Suppose that for almost all places v of F the reduction of x modulo v lies in the reduction of S modulo v. In this paper we prove that x must then lie in S + A(F)_tors. This provides a partial answer to a generalization (due to W. Gajda) of the support problem of Erdos.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2002-08-14T22:18:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G10",
      "14K15",
      "13F05"
    ],
    "keywords": [
      "abelian variety",
      "mordell-weil groups",
      "kummer theory",
      "number field",
      "partial answer"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.4064/aa110-1-6",
      "journal": "Acta Arithmetica",
      "year": 2003,
      "volume": 110,
      "number": 1,
      "pages": 77
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003AcAri.110...77W"
    }
  }
}