Cohomology of Moduli Stacks of Vector Bundles on Curves and Frobenius morphisms
University of Leicester, U.K.
After giving a brief introduction into moduli problems and moduli stacks I will indicate how to calculate the l-adic cohomology ring of the moduli stack of vector bundles on an algebraic curve in positive characteristic and explicitly describe the actions of the various geometric and arithmetic Frobenius morphisms on the cohomology ring. It turns out that using the language of algebraic stacks instead of geometric invariant theory this becomes surprisingly easy. If time permits I will indicate how to prove some analogues of the classical Weil conjectures for the moduli stack.
This will be about joint work in progress with U. Stuhler in Goettingen.