On the Motive of the Stack of Bundles

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 Poincaré 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 $|{\pi }_1(G)|$.

References in corpus (2)

• The elliptic curve in the S-duality theory and Eisenstein series for Kac-Moody groups
• Rationality criteria for motivic zeta-functions

Cited by in corpus (1)

• Motives of Deligne-Mumford Stacks