## V3A2/F4A1 Algebra II - winter term 2023/24

Dr. David Schwein

Contact:

Dr. Johannes Anschütz

Endenicher Allee 60 · Zimmer 4.027

**Tel.:** 0228-73-62216

** E-mail:** ja(add @math.uni-bonn.de)

## Time and place

Monday, 16-18h, Kleiner Hörsaal

Thursday, 14-16h, Kleiner Hörsaal

First lecture: Thursday, 12.10.2023

End of lecture period: 2.2.2023

## Content

A (nonarchimedean) local field is the Laurent series over a finite field or a finite extension of the p-adic numbers. Local fields play an important role in number theory and studying them will introduce us to several important ideas in mathematics. I plan to focus on

- Basic structure theory of local fields
- Profinite Galois theory
- Ramification theory and Newton polygons
- Galois cohomology of local fields
- Local class field theory

- V2A1 Einführung in die Algebra
- V2D1 Einführung in die Geometrie und Topologie
- V3A1/F4A1 Algebra I: Commutative Algebra.

## Literature

The course will not follow any one text linearly, but will draw on the following sources.

- J. Neukirch and A. Schmidt, Class Field Theory. The Bonn Lectures. (2013; Zbl 1282.11001)
- J.-P. Serre, Local Fields. 4th corrected edition. (2004; Zbl 1095.11504)
- F. Q. Gouvêa, p-adic numbers. An introduction. (2020; Zbl 0786.11001)
- K. Conrad, Infinite Galois theory.

## Exercise sheets

The weekly exercise sheets will be uploaded here.- Exercise sheet 1 (11.10.2023)
- Exercise sheet 2 (19.10.2023)
- Exercise sheet 3 (26.10.2023)
- Exercise sheet 4 (2.11.2023)
- Exercise sheet 5 (9.11.2023)
- Exercise sheet 6 (corrected version) (16.11.2023)
- Exercise sheet 7 (24.11.2023)
- Exercise sheet 8 (30.11.2023)
- Exercise sheet 9 (7.12.2023)
- Exercise sheet 10 (14.12.2023)
- Exercise sheet 11 (11.01.2024)
- Exercise sheet 12 (18.01.2024)
- Exercise sheet 13 (25.01.2024)

## Exercise sessions

In addition to the lecture there are weekly exercise sessions. Registration to the exercise sessions is via eCampus during the first week of the lectures. The exercise sessions themselves start in the second week of lectures.
The registration via eCampus does NOT replace the registration to the course via Basis.

Group | Time and place | Tutor | ||
---|---|---|---|---|

Group 1 | Monday, 8-10h, SR0.007 | Ruth Wild | ||

Group 2 | Monday, 10-12h, SR0.007 | Tanja Helme | ||

Group 3 | Tuesday, 8-10h, SR0.007 | Giulio Ricci |

## Exam

First exam: Wednesday, 14.2.2024, 9:00-11:00h s.t., Großer Hörsaal. Revision: 15.2., 11:30-12:30h, N0.007

Second exam: Wednesday, 13.3.2024, 9:00-11:00h s.t., Großer Hörsaal. Revision: 14.3., 11-12h, N0.007

After the end of the lectures there will be a written exam. All necessary information will be provided via this webpage during the semester. For participation in the exam a registration via Basis is necessary as well a sucessful participation in the weekly exercise sessions (more than 50% of all points).
General informations to exams can be found
here for bachelor students and
here
for master students.

*Last modified: September 2023, Johannes Anschütz*

## News

EMS Prize 2024 for Jessica Fintzen

Bonn mathematics performs excellently again in QS ranking

Stefan Schwede is invited speaker at the ECM 2024 in Sevilla

Jessica Fintzen wins Cole Prize

Regula Krapf receives university teaching award

Catharina Stroppel joined the North Rhine-Westphalia Academy for Sciences and Arts

Daniel Huybrechts receives the Compositio Prize for the periode 2017-2019

Catharina Stroppel receives Gottfried Wilhelm Leibniz Prize 2023

Grants for Mathematics students from Ukraine

Jessica Fintzen is awarded a Whitehead Prize of the London Mathematical Society

Peter Scholze elected as Foreign Member of the Royal Society