Number Theory Seminar

Let A be an abelian variety over a eld k of dimension d. In this talk I will dene a decreasing

ltration fFrgr0 of the group CH0(A) of zero cycles modulo rational equivalence which has the

property that the successive quotients are "almost" isomorphic to some Milnor-type K-groups.

Rationally the ltration coincides with the motivic ltration previously considered by A. Beauville

and S. Bloch. We will see that when k is a p-adic eld the ltration has many interesting properties.

For example, we will obtain information on the kernel of the cycle map to etale cohomology,

CH0(A)=n ! H2d(A; d

n ), where n is a positive integer. If time permits, I will also present some

work in progress, joint with K. Kato, regarding the image of the cycle map.