On the motivic class of the stack of bundles

• Autores: Kai Behrend, Ajneet Dhillon
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 212, Nº 2, 2007, págs. 617-644
• Idioma: inglés
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• Resumen

  • Let G be a split connected semisimple group over a field. We give a conjectural formula for the motivic class 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 or G=SLn. If , upon applying the Poincaré or called the Serre characteristic by some authors the formula reduces to results of Teleman and Atiyah¿Bott on the gauge group. If , upon applying the counting measure, it reduces to the fact that the Tamagawa number of G over the function field of C is |p1(G)|.