Mathematical Institute of the University of Bonn

Algebra II - Wintersemester 2016/17

Prof. Dr. Michael Rapoport

Contact:
Dr. Judith Ludwig
Endenicher Allee 60 · Office 4.025
Tel.: 0228-73-62244
E-mail: jludwig (add @math.uni-bonn.de)

Time and Place

Monday 12-14h, großer Hörsaal, Wegerlerstraße 10, Thursday 14-16h , kleiner Hörsaal, Wegelerstraße 10.
First Lecture: Monday 17.10.2016.

Content of the course

The subject matter of the course is "Algebraic Number Theory". This means that we will study the arithmetic of the rings of integers in finite extensions of ℚ or 𝔽_p[X], and their local analogues ℚ_p or 𝔽_p⟦X⟧. Highlights will be: the prime ideal decomposition in Dedekind rings, the finiteness of class groups, the Dirichlet unit theorem, Hilbert ramification theory, density of ideals in an ideal class, the Dedekind zeta function and the distribution of prime ideals, the class number formula.

The prerequisites are:

• Basic concepts of Commutative Algebra, in particular localization, completion, going up/down (the book ”Commutative Algebra” by Atiyah/Macdonald contains more than necessary).
• Later some knowledge of Complex Function Theory.

Literature

• J. Neukirch: Algebraic number theory, Springer
• E. Hecke: Lectures on the theory of algebraic numbers, Springer
• G. Janusz: Algebraic number fields, Am. Math. Soc.
• P. Samuel: Algebraic theory of numbers, Houghton Muffin Co.

Exercise sessions

There are weekly exercise sessions accompanying the lecture. It is necessary to attend the exercise sessions and hand in solutions to the exercises in order to participate in the final exam. Please hand in your solutions mondays during the lecture. Registration for the exercise sessions takes place during the first lecture. The exercise sessions start in week two.

Group	Time and Place	Tutor
Group 1	Wednesday 16-18 Uhr, Room 0.008	Samed Düzlü
Group 2	Friday 12-14 Uhr, Room 0.008	Georg Linden

The room numbers refer to the building Mathematik Zentrum, Endenicher Allee 60.

Exercises

• Exercise sheet 1 vom 17.10.2016
• Exercise sheet 2 vom 24.10.2016
• Exercise sheet 3 vom 31.10.2016
• Exercise sheet 4 vom 07.11.2016
• Exercise sheet 5 vom 14.11.2016
• Exercise sheet 6 vom 21.11.2016
• Exercise sheet 7 vom 28.11.2016
• Exercise sheet 8 vom 05.12.2016
• Exercise sheet 9 vom 12.12.2016
• Exercise sheet 10 vom 19.12.2016
• Bonus sheet vom 19.12.2016
• Exercise sheet 11 vom 16.01.2017
• Exercise sheet 12 vom 23.01.2017
• Exam vom 09.02.2017, Outline of solutions.

Exams

The exam took place on Thursday, 09.02.2017 from 14:00 to 16:00. The post-exam review (where you can view your exam to see your mistakes, check whether the points have been added correctly, etc.) took place on Friday, 10.02.2017 from 09:00 to 10:00 in the Hausdorffraum.

The resit exam will take place on Saturday, 25.03.2017 from 09:00 to 11:00. The location is: Großer Hörsaal, Wegelerstraße 10.

Last modified: 10. 02. 2017, Judith Ludwig