
University of SydneySchool of Mathematics and StatisticsComputational Arithmetic Geometry Seminar15:00  16.00 (+ epilogue until 16.30) in Carslaw 709 on Thursday 7 February
Martin BrightComputing the BrauerManin obstructionSome families of Diophantine equations, such as quadratic forms, have a very useful property: if an equation has solutions in the real numbers and in each padic field, then it has a rational solution. Such families of equations are said to satisfy the Hasse principle. In general the Hasse principle does not hold, but many violations are described by the socalled BrauerManin obstruction. This obstruction was first defined by Manin and is based on the Brauer group of the variety. In this talk I will define the Brauer group of a variety and explain Manin's obstruction to the Hasse principle. I will then show how the obstruction may be calculated for a certain family of surfaces. 