Pure Maths Colloquium: Cohomology of moduli of vector bundles on algebraic curves and Frobenius morphisms
23 May 2011 17:15 in CM221
After a general introduction to moduli problems and moduli stacks, I will explain how to calculate the cohomology ring of the moduli stack of vector bundles on a fixed algebraic curve in positive characteristic. This gives a unified view on classical results of Atiyah-Bott and Harder-Narasimhan. I will then discuss actions of various Frobenius morphisms and indicate how to prove an analogue of the classical Weil conjectures for this moduli stack, which basically gives a "stacky" count of the number of isomorphism classes of vector bundles on the fixed algebraic curve. This is joint work in progress with U. Stuhler (Goettingen).
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