Number Theory III: Class Field Theory - Winter term 2016/17
Zeit: Dienstags, 8:30-10 Uhr und 14-16 Uhr
Ort: Arnimallee 6 SR 032/A6
Übungstermin: Fridays 8:15-9:45am, Arnimallee 6 SR032/A6 (time change!)
Exam: February 14, 2017, 8:00am to 10:00am
Literatur:
Goal of the course shall be to prove the main theorem of local class field theory. To this aim, we shall cover:
- Infinite Galois theory
- Local fields
- Brauer groups
- Brauer groups of local fields
- Definition of local Artin map
- 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
Files
Notes
Exercises
- Problem set 1, return by Oct. 26
- Problem set 2, return by Nov. 1 (typo in Ex. 2f corrected, Oct. 30, 17:38)
- Problem set 3, return by Nov. 8 (new version with two corrections, Nov. 4, 11:30)
- Problem set 4, return by Nov. 15
- Problem set 5, return by Nov. 23 (typo corrected in hint for ex. 1a)
- Problem set 6, return by Nov. 29
- Problem set 7, return by Dec. 7
- Problem set 8, return by Dec. 14
- Problem set 9, return by Jan. 3 (typo in Ex. 2.b corrected, Dec. 18) Addendum
- Problem set 10, return by Jan. 10
- Problem set 11, return by Jan. 17
- Problem set 12, return by Jan. 24
- Problem set 13, return by Jan. 31
- Problem set 14, return by Feb. 7