{
  "id": "1009.6191",
  "version": "v2",
  "published": "2010-09-30T16:53:00.000Z",
  "updated": "2011-05-16T19:47:23.000Z",
  "title": "Very stable extensions on arithmetic surfaces",
  "authors": [
    "Soulé Christophe"
  ],
  "comment": "This paper has been withdrawn since both theorems claimed in it are incorrect",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "Given a line bundle L on a smooth projective curve over the complex numbers, we show that a general extension E of L by the trivial line bundle is very stable: line bundles contained in E have degree much less than half the degree of E. From this result we deduce new inequalities for the successive minima of the euclidean lattice H^1(X,L^{-1}), where L is an hermitian line bundle on the arithmetic surface X.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-05-16T19:47:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14H60",
      "14G40"
    ],
    "keywords": [
      "arithmetic surface",
      "stable extensions",
      "trivial line bundle",
      "hermitian line bundle",
      "complex numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1009.6191C"
    }
  }
}