AMCA: On Chow and Brauer groups of surfaces over local fields by Takao Yamazaki

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Canadian Number Theory Association VIII Meeting
June 20-25, 2004
The Fields Institute
Toronto, ON, Canada

Organizers
John Friedlander (Toronto) and Cam Stewart (Waterloo)

On Chow and Brauer groups of surfaces over local fields
by
Takao Yamazaki
Institute of Mathematics, University of Tsukuba

We shall consider the following problems concerning the Chow group CH₀(X) of a surface X over a local field: (A) How does CH₀(X) look like (as an abelian group)? (B) There is a canonical homomorphism which relates CH₀(X) to the dual of the Brauer group Br(X) of X. How close is this to be an isomorphism? Both problems are studied by many authors, mainly in case the geometric genus p_g(X) of X is zero. Here, we consider the case where X is a product of two Tate elliptic curves, so that p_g(X)=1. We shall see that (A) the structure of CH₀(X) looks very differently from the case of p_g(X)=0, but (B) the relation to the Brauer group remains fairly similar.

Date received: April 25, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts. Document # calz-65.