Because of the attack on the computer network of the University of Duisburg-Essen, some content (in particular some image files) cannot be accessed because it is stored on central servers of the university.

# Algebraic Groups and Class Fields

**Suggested time:** Mo 14-16:00, Room WSC-S-U-3.01

*If you are interested in this course please send me an email, so that we can find a time that suits all potential participants.*

**First meeting:** Mo 7.4.2014.

**Content:** The course will essentially follow the classic book of J.-P. Serre of the same title:

J.-P. Serre, Algebraic Groups and Class Fields, Springer GTM 117.

The standard references for algebraic geometry have changed since this book was written and I will simply (?) try to adapt the language accordingly.

The main aim of the book is to prove a geometric version of class field theory for varieties following Rosenlicht and Lang.

Along the way this includes the construction of generalized Jacobians.

**Zielgruppe:** PhD and master students having followed courses on algebraic geometry.

**Prerequisites:** I will try to adjust to the needs of the audience, but would like to assume that you are - to some extend - comfortable with the language of algebraic geometry as taught in a 2 semester course, i.e., you should know what schemes, coherent sheaves and line bundles are and ideally you would also have seen cohomology of coherent sheaves before.

Exercises can be found on the moodle page of the course.