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 CH0(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 ├ętale 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.

Other Information: 

10th Anniversary Speaker Series 2007