{
  "id": "math/0512640",
  "version": "v1",
  "published": "2005-12-29T17:44:11.000Z",
  "updated": "2005-12-29T17:44:11.000Z",
  "title": "On the Motive of the Stack of Bundles",
  "authors": [
    "Kai Behrend",
    "Ajneet Dhillon"
  ],
  "categories": [
    "math.AG"
  ],
  "abstract": "Let $G$ be a split connected semisimple group over a field. We give a conjectural formula for the motive of the stack of $G$-bundles over a curve $C$, in terms of special values of the motivic zeta function of $C$. The formula is true if $C=\\pp^1$ or $G=\\sln$. If $k=\\cc$, upon applying the Poincar\\'e or Serre characteristic, the formula reduces to results of Teleman and Atiyah-Bott on the gauge group. If $k=\\ffq$, upon applying the counting measure, it reduces to the fact that the Tamagawa number of $G$ over the function field of $C$ is $|\\pi_1(G)|$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-29T17:44:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "motivic zeta function",
      "split connected semisimple group",
      "function field",
      "tamagawa number",
      "gauge group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12640B"
    }
  }
}