### Local-global principle for zero-cycles of degree one and integral Tate conjecture for 1-cycles

Colliot-Thélène, JL *(Paris-Sud 11 )*

Monday 24 August 2009, 10:00-11:00

Seminar Room 1, Newton Institute

#### Abstract

Shuji Saito showed that an integral version of the Tate conjecture for 1-dimensional cycles on a variety over a finite field essentially implies that the Brauer-Manin obstruction to the existence of a zero-cycle of degree 1 on varieties over a global function field (function field in one variable over a finite field) is the only obstruction. In this talk we describe some known results about integral versions of the Tate conjecture, and we give two applications, one of which comes from joint work with T. Szamuely.

#### Presentation