{
  "id": "1412.7697",
  "version": "v1",
  "published": "2014-12-24T16:02:36.000Z",
  "updated": "2014-12-24T16:02:36.000Z",
  "title": "Defect of an extension, key polynomials and local uniformization",
  "authors": [
    "Jean-Christophe San Saturnino"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "For all simple and finite extension of a valued field, we prove that its defect is the product of the effective degrees of the complete set of key polynomials associated. As a consequence, we obtain a local uniformization theorem for valuations of rank 1 centered on an equicharacteristic quasi-excellent local domain satisfying some inductive assumptions of lack of defect.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-24T16:02:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "polynomials",
      "equicharacteristic quasi-excellent local domain satisfying",
      "local uniformization theorem",
      "complete set",
      "finite extension"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.7697S"
    }
  }
}