{
  "id": "math/0403389",
  "version": "v1",
  "published": "2004-03-23T19:14:08.000Z",
  "updated": "2004-03-23T19:14:08.000Z",
  "title": "On the existence of a torsor structure for Galois covers",
  "authors": [
    "Saidi Mohamed"
  ],
  "comment": "These notes are not intended for publication",
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $R$ be a complete discrete valuation ring with residue characteristic $p>0$. In this note we give an example of a Galois cover $f:Y\\to X$ between flat and normal formal $R$-schemes of finite type which is \\'etale above the generic fibre of $X$ such that the special fibre of $Y$ is reduced and such that $f$ doesn't have the structure of a torsor under a finite and flat $R$ group scheme. In the example $R$ has equal characteristic $p$ and the Galois group of the cover is cyclic of order $p^2$. In the example the formal scheme $X$ is affine and can be choosen to be even smooth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-03-23T19:14:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "galois cover",
      "torsor structure",
      "equal characteristic",
      "formal scheme",
      "group scheme"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3389M"
    }
  }
}