# Algebraic Number Theory 2 (Class Field Theory)

**Lecture:**

Monday 4 - 6 pm, WSC-U-3.01

Wednesday 4 - 6 pm, WSC-U-3.01

**Problem Session:**

Thursday, 8:30 - 10:00 am, WSC-U-3.01

**Prerequisites**

The lecture is largely independent of Algebraic Number Theory 1. However, I do expect the participants to be well acquainted with the techniques provided by an introductory course on abstract algebra. This lecture is part of our ALGANT Master Program and will be given in English.

**Content**

Algebraic number theory studies the field of rational numbers and its finite field extensions, the so-called algebraic number fields. Completing an algebraic number field with respect to a nontrivial absolute value yields what is known as a local field, e.g. the real or the p-adic numbers.

Class field theory deals with the problem of classifying all abelian extensions of a nonarchimedean local field or an algebraic number field, i.e. all Galois extensions with abelian Galois groups. Initially, this problem was solved by Hasse, Artin and many others. It is of great importance up to the present day.

**Electronic Class Room**

There is an electronic class room on the Moodle platform containing much more information and all the learning material. Read backward, the password needed to subscribe is

2202eSoS2yroehTrebmuNciarbeglA