## Chow group of 0-cycles on a surface over a p-adic field with infinite torsion subgroup

- Date: 04/30/2007

Shuji Saito (University of Tokyo)

University of Alberta

In this talk I would like to demonstrate how Hodge theory can play a

crucial role in an arithmetic question. The issue is to construct an

example of a projective smooth surface *X* over a *p*-adic field *K* such that for any prime *l* different from *p*, the *l*-primary torsion subgroup of *CH*0(*X*), the Chow group of 0-cycles on *X*, is infinite. A key step in the proof is disproving a variant of the Bloch-Kato conjecture which characterizes the image of an *l*-adic regulator map from a higher Chow group to a continuous étale cohomology of *X* by using *p*-adic

Hodge theory. By the aid of the theory of mixed Hodge modules, we

reduce the problem to showing the exactness of de Rham complex

associated to a certain variation of Hodge structure, which follows

from Nori's connectivity theorem.

10th Anniversary Speaker Series 2007