Dennis Gaitsgory - Tamagawa Numbers and Nonabelian Poincare Duality, II [2013]

Dennis Gaitsgory Wednesday, August 28 4:30PM Tamagawa Numbers and Nonabelian Poincare Duality, II Gelfand Centennial Conference: A View of 21st Century Mathematics MIT, Room 34-101, August 28 - September 2, 2013 Abstract: This will be a continuation of Jacob Lurie’s talk. Let X be an algebraic curve over a finite field Fq and let G be a group scheme over X, which is generically semi-simple and simply connected. Weil’s formula for the volume of the adelic quotient corresponding to G will be interpreted as a formula for the number of points over Fq of the moduli stack Bun(G) of G-bundles on X. By applying the Lefschetz trace formula, it will be shown that Weil’s formula for the number of points follows from the Atiyah-Bott formula for the cohomology of Bun(G). The Atiyah-Bott formula is a local-to-global expression for the cohomology, and we will prove it using an algebro-geometric version of non-abelian Poincare duality; specifically, by uniformizing Bun(G) by the affine Grassmannian of G. http://math.mit.edu/conferences/Gelfa...