Weil's conjecture on Tamagawa numbers for function fields
Weil's conjecture on Tamagawa numbers for function fields
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Amina Abdurrahman, Princeton University
We sketch some beautiful topological ideas in Gaitsgory's and Lurie'sÌýproof of Weil's conjecture for function fields (2014).ÌýWe first discuss how the Siegel mass formula which counts particularÌýequivalence classes of quadratic forms motivates the conjecture forÌýnumber fields (entirely proven in 1988).ÌýGaitsgory and Lurie reformulate the conjecture for function fields asÌýa similar counting problem of principal G-bundles on an algebraicÌýcurve X and reduce the problem to understanding the topology of theÌýspace that these bundles give rise to. We discuss differentÌýformulations of Weil's conjecture and a topological local-to-globalÌýprinciple that is used to compute the cohomology of the moduli stackÌýof G-bundles on X.