250125 VO Selected topics in number theory (2012S)

The course gives an introduction to the theory of algebraic curves. The emphasis will be on the connections with algebraic number theory. On the one hand Algebraic curves can be studied with methods which are analogous to methods in algebraic number theory; on the other hand the study of such curves solves important problems in algebraic number theory. Examples for this are given by the zetafunction of algebraic curves which is defined in analogy with the zeta function of a number field and the construction of extensions of number fields using ellitpic curves. We want to adress both these problems in the course. Prerequisites are knowledge of basic notions of algebraic number theory and algebraic geometry.