On the Motive of the Stack of Bundles
نویسنده
چکیده
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 = P or G = SLn. If k = C, upon applying the Poincaré or Serre characteristic, the formula reduces to results of Teleman and Atiyah-Bott on the gauge group. If k = Fq, upon applying the counting measure, it reduces to the fact that the Tamagawa number of G over the function field of C is |π1(G)|.
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