Goal of the course shall be to prove the main theorem of local class field theory. To this aim, we shall cover:

1. Infinite Galois theory
2. Local fields
3. Brauer groups
4. Brauer groups of local fields
5. Definition of local Artin map
6. Proof of the main theorem.

Our references shall be:

• [Milne1] for 2.
• [Milne2] for 1. and partly for 3.
• [KKS] for 3., 4., 5., 6.

Milne’s books are freely available on the web, we shall provide the book Kato-Kurokawa-Saito.

• [Milne1]: Milne, James: Algebraic Number Theory (available here)
• [Milne2]: Milne, James: Class Field Theory (available here)
• [KKS]: Kato, K., Kurokawa, N. and Saito, T.: Number Theory 2: Introduction to Class Field Theory, Translations of Mathematical Monographs Volume 240

Literatur:

https://www.jmilne.org/math/CourseNotes/CFT.pdf