# Cyclotomic Fields and Iwasawa Theory

#### Content of the course

In 1850, Kummer proved that the p-part of the class group of the cyclotomic field Q(ζp) is trivial, if and only if the prime p does not appear in the numerator of any Bernoulli number. This can be seen as the starting point of Iwasawa Theory, which relates p-adic L-functions to p-parts of class groups in Zp extensions. In this course, we would like to give an introduction to this beautiful theory in the cyclotomic case. We will give a more detailed overview in the first lecture.

#### Schedule:

Lectures:

- Monday 12:15-13:45 in WSC-S-U-3.03

- Wednesday 12:15-13:45 in WSC-S-U-3.03

Exercises (Bence Forrás):

- Wednesday 14:15-15:45 in WSC-S-U-3.03

#### Moodle

For more information, please, see the Moodle page of this course (the password is the name of a Japanese mathematician in the title of the lecture).

Please, do not hesitate to contact me if you have any questions.