Algebra II -- Algebraic Number Theory -- WS20/21 Lecturer: Dr. Johannes Anschütz

Contact:
Dr. Andreas Mihatsch
Endenicher Allee 60 · Room 4.024
Tel.: 0228-73-62369
E-mail: mihatsch (ergänze @math.uni-bonn.de)


Time and Place

Mondays 12:15 pm -- 2 pm and Thursdays 2:15 pm -- 4 pm (Starts Monday, Oct 26)
Via Zoom. Link can be obtained through eCampus.


Exercise Sheets

Solutions may be handed in in pairs. Half the points are needed to take the exam.

Sheet 1, due October 31
Sheet 2, due November 7
Sheet 3, due November 14
Sheet 4, due November 21
Sheet 5, due November 28
Sheet 6, due December 5
Sheet 7, due December 12
Sheet 8, due December 19
Sheet 9, due January 9
Sheet 10, due January 16
Sheet 11, due January 23
Sheet 12, due January 30
Sheet 13, due February 6


Lecture Notes

These are the write-ups from the Zoom lectures.

Week 1 -- October 26 and October 29
Week 2 -- November 2 and November 5

Week 3 -- Due to a conference the lecturer attends, there will be no live lectures this week. Please work through Section 2.2 of Tian's manuscript yourself along these instructions and with this explanatory Video (password is a permutation of kindDede) plus its notes. Lectures resume on November 16.

Week 4 -- November 16 with Question Session and November 19 found here and here
Week 5 -- November 23 and November 26
Week 6 -- November 30 and December 3
Week 7 -- December 7 and December 10
Week 8 -- December 14 and December 17
Week 9 -- Lecture for Christmas Week has been recorded. See here for the video and its notes. (Password is the same permutation of kindDede.)
-- Christmas Break --
Week 10 -- January 7
Week 11 -- January 11 and January 15
Week 12 -- January 18 and January 21
Week 13 -- January 25 and January 28
Week 14 -- February 1 and February 4
Week 15 -- February 8 and February 11


Use of eCampus

Please register on eCampus to

  • obtain the Zoom link for lectures,
  • join exercise session groups,
  • upload your solutions for exercise sheets and
  • obtain their corrections.
Please note that you additionally have to register on BASIS (both for the lecture and for the exercise session).


Content of the course

The course follows the manuscript of Yichao Tian. Its content may 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

  • J.W.S. Cassels, A.Fröhlich: Algebraic Number Theory, London Mathematical Soc.
  • 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.

Exercise session

There are four weekly exercise session groups. It is necessary to join one and to hand in solutions to the weekly sheets to participate in the final exam. Registration for the exercise sessions takes place on eCampus.

Exercise sessions start on Oct 27 and 28, respectively. The first meeting will be a recap of some aspects of algebra such as Galois theory.

Group Time Tutor
Group 1 Tuesdays 10:15 am Lucas Mann
Group 2 Tuesdays 12:15 pm Axel Kölschbach
Group 3 Wednesdays 10:15 am Matthias Storzer
Group 4 Wednesdays 12:15 pm Robin Louis


Examination

The examination will be oral and held over Zoom. The first round of oral exams takes place on March 1 and 2, the second round on March 29 and 30. Detailed information will be sent to all registered (via Basis) students in time.