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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

15:00 - 16.00 (+ epilogue until 16.30) in Carslaw 709 on Thursday 7 February

Martin Bright

Computing the Brauer-Manin obstruction

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.