Séminaires doctorant à venir

In this talk, I will give a short introduction to the classical theory of heights and some of its applications in Diophantine geometry. In Diophantine geometry one is trying to study the solutions of Diophantine equations by algebro-geometric methods. One of the tools used for this are heights. The height of an algebraic number can be considered as a measurement of its complexity. Heuristically, it is proportional to the number of bits needed to store a given number on a computer. The theorem of Northcott states that in a fixed number field there are only finitely many numbers whose height is smaller than a given bound. This makes heights useful tool to limit the number of solutions of a Diophantine equation.