{
  "id": "math/0505079",
  "version": "v1",
  "published": "2005-05-04T17:53:22.000Z",
  "updated": "2005-05-04T17:53:22.000Z",
  "title": "Semi-stable extensions on arithmetic surfaces",
  "authors": [
    "C. Soule"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "On a given arithmetic surface, inspired by work of Miyaoka, we consider vector bundles which are extensions of a line bundle by another one. We give sufficient conditions for their restriction to the generic fiber to be semi-stable. We then apply the arithmetic analog of Bogomolov inequality in Arakelov theory, and deduce from it a lower bound for some successive minima in the lattice of extension classes between these line bundles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-05-04T17:53:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G40"
    ],
    "keywords": [
      "arithmetic surface",
      "semi-stable extensions",
      "line bundle",
      "generic fiber",
      "extension classes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......5079S"
    }
  }
}