Torsten Wedhorn: The tautological ring for Shimura varieties

Abstract:
Shimura varieties play a central role in modern arithmetic geometry. Their Chow ring is still very mysterious. In this talk I explain the definition of a certain subring, the tautological ring. This ring is a quotient of (conjecturally even equal to) a purely combinatorial object and can therefore in principle be understood. On the other hand it contains all "interesting" cycle classes. I will explain this and how to relate such classes for good reductions of Shimura varieties of Hodge type. The guiding example is the modular curve or, more generally, the moduli space of principally polarized abelian varieties.