Counting failures of a local-global principle

Rachel Newton (University of Reading)

Wednesday 30th October 16:00-17:00 Maths 311B

Abstract

Methods for solving polynomial equations in the integers and rationals have been sought and studied for thousands of years. Modern approaches try to piece together 'local' (meaning real and p-adic) information to decide whether a polynomial equation has a 'global' (meaning rational) solution. I will describe this approach and its limitations, with the aim of quantifying how often the local-global method fails within families of polynomial equations arising from the norm map between fields, as seen in Galois theory. This is joint work with Tim Browning.

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