
University of SydneySchool of Mathematics and StatisticsComputational Arithmetic Geometry Seminar10:05  10.55 (+ epilogue until 11.30) in Carslaw 453 on Friday 11 April
Victor ScharaschkinBrauerManin for 0cyclesLet 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 BrauerManin obstruction attempts to account for this failure. These ideas can be generalized to the case of 0cycles, and ColliotThelene has conjectured that the BrauerManin obstruction should be the only obstruction to the Hasse Principle for 0cycles of degree 1. We prove that a slightly weaker statement is true, assuming that the TateShafarevich group of the Albanese of X is finite. 