Room 326

Local class field theory

Denis Benois

University of Bordeaux

In this course we give a self-contained exposition of the local class field theory using the homological algebra. The local class field theory gives a description of abelian extension of local fields and their arithmetical properties. The following topic will be covered:
1. Complexes and homology.
2. Derived functors
3. Cohomology and homology of groups.
4. Tate exact sequence
5. Local class field theory: main theorems
6. The theory of Lubin-Tate.