{
  "id": "math/0306339",
  "version": "v2",
  "published": "2003-06-24T08:26:54.000Z",
  "updated": "2004-04-16T13:43:11.000Z",
  "title": "Discrete invariants of varieties in positive characteristic",
  "authors": [
    "B. Moonen",
    "T. Wedhorn"
  ],
  "comment": "35 pages, minor changes in exposition, major changes to introduction",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "If $S$ is a scheme of characteristic $p$, we define an $F$-zip over $S$ to be a vector bundle with two filtrations plus a collection of semi-linear isomorphisms between the graded pieces of the filtrations. For every smooth proper morphism $X\\to S$ satisfying certain conditions the de Rham bundles $H^n_{{\\rm dR}}(X/S)$ have a natural structure of an $F$-zip. We give a complete classification of $F$-zips over an algebraically closed field by studying a semi-linear variant of a variety that appears in recent work of Lusztig. For every $F$-zip over $S$ our methods give a scheme-theoretic stratification of $S$. If the $F$-zip is associated to an abelian scheme over $S$ the underlying topological stratification is the Ekedahl-Oort stratification. We conclude the paper with a discussion of several examples such as good reductions of Shimura varieties of PEL type and K3-surfaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-04-16T13:43:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14J10",
      "14F40",
      "14J28",
      "11G18",
      "14K10",
      "20G40"
    ],
    "keywords": [
      "discrete invariants",
      "positive characteristic",
      "smooth proper morphism",
      "vector bundle",
      "semi-linear isomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......6339M"
    }
  }
}