Jürg Kramer: Irrationality of √2 and Arakelov Geometry

Starting with the well-known proof of the irrationality of √2, we would like to show in our talk how this proof has significantly influenced the development of modern Diophantine Geometry. A key notion in this respect is the height of a rational point on an algebraic curve or, more generally, on an algebraic variety. It will be shown how this notion can be used to derive results on the set of rational points on algebraic varieties and how it can be further generalized by means of Arakelov Geometry to higher dimensional objects in order to measure their arithmetic complexity.