Computational Arithmetic Geometry Seminar

Some 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 p-adic 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 so-called Brauer-Manin 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.