Andrea Miller (Harvard)

"On a Conjecture of Murre for some mixed Shimura varieties"

Abstract: In the first part of my talk I will give a short introduction to Shimura varieties and Chow motives and recall some of their properties. I will then state a conjecture of J.Murre concerning a motivic decomposition of the Chow-motive of a smooth projective variety. This yields a strengthening of Grothendieck's conjecture C for rational equivalence. In the last part I will show how to prove this conjecture in the case of a universal 9-dimensional abelian variety (with additional structure) over a unitary Shimura variety.