Failure of strong approximation on an affine cone
Heilbronn Number Theory Seminar
4th October 2017, 4:00 pm – 5:00 pm
Howard House, 4th Floor Seminar Room
The equation X_0^2 + 47 X_1^2 = 103 X_2^2 + 82297 X_3^2 has
the following curious property: of its solutions modulo 17, only half
can be lifted to a solution in coprime integers. I will show how to
explain this phenomenon using the Brauer-Manin obstruction to strong
approximation on the punctured affine cone described by the equation.
This is joint work with Ivo Kok.