Mathematical Institute of the University of Bonn

Algebraic Number Theory - Winter Term 2017/18

Prof. Dr. Yichao Tian

Contact:
Dr. Johannes Anschütz
Endenicher Allee 60 · Zimmer 4.027
Tel.: 0228-73-62216
E-mail: ja (ergänze @math.uni-bonn.de)

Time and Place

Monday, 16-18h, Kleiner Hörsaal
Thursday, 10-12h, Kleiner Hörsaal
First Lecture: Thursday 12.10.2017.

Content of the course

The content of this course can roughly be divided into three parts.
1. Basic properties of integral rings of number fields, decomposition of primes in extensions, and Minkowski’s bound of class numbers.
2. Dedekind zeta functions, Dirichlet L-series, distribution of ideals and the residue formula.
3. Non-archimedean fields, adeles and Tate’s thesis.

Literature

H.Davenport: Multiplicative Number Theory GTM 74. Springer.
S. Lang: Algebraic Number Theory GTM 110, Springer.
D. Marcus: Number Fields, 1977, Springer.
L. Washington: Introduction to Cyclotomic Fields, 1996, Springer.
J.P. Serre: Local Fields GTM 67. Springer.
J.W.S. Cassels, A.Fröhlich: Algebraic Number Theory, London Mathematical Soc.

Exams

The oral exams will take place from Monday, 05.02.2018, till Wednesday, 07.02.2018. The students are asked to sign up in a time schedule during the lecture course to arrange a date. Please contact the lecturer or the assistant if any of the above dates cannot be attended. The second date for the oral exams will be on Thursday, 22.3.2018. Participants of the second exam are asked to contact the lecturer or the assistant in the beginning of March. The official informations on registration and examination of graduate course modules can be found here.

Exercise sheets

Exercise sheet 1 (16.10.2017)
Exercise sheet 2 (23.10.2017)
Exercise sheet 3 (30.10.2017)
Exercise sheet 4 (06.11.2017)
Exercise sheet 5 (13.11.2017)
Exercise sheet 6 (20.11.2017)
Exercise sheet 7 (27.11.2017)
Exercise sheet 8 (04.12.2017)
Exercise sheet 9 (11.12.2017)
Exercise sheet 10 (18.12.2017)
Exercise sheet 11 (08.01.2018)
Exercise sheet 12 (15.01.2018)
Exercise sheet 13 (22.01.2018)

Exercise session

There are two weekly exercise sessions accompanying the lecture. It is necessary to attend one exercise session and hand in solutions to the exercises in order to participate in the final exam. Please hand in your solutions mondays during the lecture. The regular exercise sessions start in week two. Registration for the exercise sessions takes place during the first lectures or exercise sessions. Please note that this does not replace the registration for the course module in BASIS (which includes a different registration for the exercise session) during the registration period in december.