University Crest
School of Mathematics and Statistics
Computational Algebra Group

Carslaw building

Algebra Seminar
Algebraic Geometry Seminar
Computational Algebra Seminar
Other Seminars


University of Sydney

School of Mathematics and Statistics

Computational Arithmetic Geometry Seminar

10:05 - 10.55 (+ epilogue until 11.30) in Carslaw 453 on Friday 11 April

Victor Scharaschkin

Brauer-Manin for 0-cycles

Let X be a variety defined over Q. Even if X has points in every local field, it still may not have any global points: the Hasse Principle may fail. The Brauer-Manin obstruction attempts to account for this failure. These ideas can be generalized to the case of 0-cycles, and Colliot-Thelene has conjectured that the Brauer-Manin obstruction should be the only obstruction to the Hasse Principle for 0-cycles of degree 1. We prove that a slightly weaker statement is true, assuming that the Tate-Shafarevich group of the Albanese of X is finite.