# Dick Hain (Duke University)

## Friday 17th May, 2:30-3:20pm, Carslaw 273

### The Beauville splitting of the Chow groups of the Jacobian of a general curve

Beauville showed that the Chow ring (tensored with the rationals) of an abelian variety splits into eigenspaces under multiplication by an integer $$m>1$$. It it not well understood how many of these eigenspaces can be non-zero. In this talk I will give a preliminary report on work whose goal is to show that almost all eigencomponents of the class of a general curve (of sufficiently high genus) in its Jacobian are non-zero. This work makes essential use of recent work of Church and Farb on the homology of Torelli groups.