Dennis Gaitsgory - The Tamagawa number formula over function fields

Séminaire Paris Pékin Tokyo / Mercredi 17 novembre 2015 Let G be a semi-simple and simply connected group and X an algebraic curve. We consider Bun_G(X), the moduli space of G-bundles on X. In their celebrated paper, Atiyah and Bott gave a formula for the cohomology of Bun_G, namely H^*(Bun_G)=Sym(H_*(X)\otimes V), where V is the space of generators for H^*_G(pt). When we take our ground field to be a finite field, the Atiyah-Bott formula implies the Tamagawa number conjecture for the function field of X.