{
  "id": "math/0701903",
  "version": "v1",
  "published": "2007-01-31T16:39:48.000Z",
  "updated": "2007-01-31T16:39:48.000Z",
  "title": "Essential dimension and algebraic stacks",
  "authors": [
    "Patrick Brosnan",
    "Zinovy Reichstein",
    "Angelo Vistoli"
  ],
  "comment": "52 pages",
  "categories": [
    "math.AG"
  ],
  "abstract": "We define and study the essential dimension of an algebraic stack. We compute the essential dimension of the stacks Mgn and MgnBar of smooth, or stable, n-pointed curves of genus g. We also prove a general lower bound for the essential dimension of algebraic groups with a non-trivial center. Using this, we find new exponential lower bounds for the essential dimension of spin groups and new formulas for the essential dimension of some finite p-groups. Finally, we apply the lower bound for spin groups to the theory of the Witt ring of quadratic forms over a field k.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-01-31T16:39:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14A20",
      "20G15",
      "11E04",
      "14H10"
    ],
    "keywords": [
      "essential dimension",
      "algebraic stack",
      "spin groups",
      "exponential lower bounds",
      "general lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 52,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007math......1903B"
    }
  }
}