## Breadcrumb

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

## Topic

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 Ã©tale 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.
This is a Past Event

Event Type

**Scientific, Seminar**

Date

**April 30, 2007**

Time

2:00am
- 3:00am

Location

University of Alberta