KTH/SU Mathematics Colloquium
September 9, 2009
Jürg Kramer, Humboldt University, Berlin
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.