On the Motive of the Stack of Bundles

Details On the Motive of the Stack of Bundles On the Motive of the Stack of Bundles

2005-12-29

arxiv.org/abs/math/0512640v1

Mathematics

Algebraic Geometry

Scientific paper

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 $|\pi_1(G)|$.

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