: École d’Été 2017 - Géométrie d'Arakelov et applications diophantiennes

The distribution of rational points of bounded height on algebraic varieties is far from uniform. Indeed the points tend to accumulate on thin subsets which are images of non-trivial finite morphisms. The problem is to find a way to characterise these thin subsets. The slopes introduced by Jean-Benoît Bost are a useful tool for this problem. These lectures will present several cases in which this approach is fruitful. We shall also describe the notion of locally accumulating subvarieties which arise when one considers rational points of bounded height near a fixed rational point