On a question of Colliot-Thélène on Chow group mod $n$

Abstract

In this note we define the notion of Tate-Shafarevich group and Selmer group of the Chow group of an abelian variety defined over a number field. In this context we give positive answer to the question of Colliot-Thélène that the Chow group of zero cycles modulo $n$ is finite over any number field.

arXiv comment21 pages, title and abstract changed, a few typos corrected, comments are welcome