442503 VO Class field theory (2016S)

The theme of class field theory is to understand the the entity of all abelian extensions L of a given number field K (i.e. L/K is a galois extension with abelian galois group). The central result of the theory is the Artin reciprocity law, which yields a description of the Galois group of an abelian extension L by data which depend on L but which are contained in the base field K. This reciprocity law is a fundamental result of number theory (it includes a generalization of the quadratic reciprocity law to higher degrees) with connections to many methods and areas of mathematics. Accordingly there are very different approaches to a proof (similar to the quadratic reciprocity law).
We want to present a proof that combines analytic and algebraic methods.

The course is a continuation of the course "Algebraische Zahlentheorie" held in WS 2015; hence, prerequisites are basic knowledge of Algebraic number theory.