Topics in Algebraic Number Theory
The main part of the course follows the notes written by Stevenhagen.
Lectures and exercise classes both will be held in person, in the Mathematical Institute (Snellius building). Students from outside Leiden are welcome, and should register officially. If you would like to audit the course without registering, please contact the lecturers via email to be added to the mailing list. The weekly schedule for this course is:
| Lectures (Rosu/Vonk) | Snellius 402 | Fridays 11:00 - 12:45 |
| Exercises (Daas) | Snellius 402 | Fridays 13:15 - 15:00 |
Registered students who are taking this course for credit are required to hand in weekly homework assignments, which count for 20% of the final grade. Every Friday after the lecture, a short list of problems will be announced on this webpage, two of which are due to be handed in by 11.59 pm the day before the next lecture. You have free choice which two problems from the list you decide to hand in for grading each week. Handing in your solutions can be done by sending an email to Mike Daas with your typeset solutions attached. There is a final oral exam whose outcome constitutes 80% of the overall grade.
Lectures
Below is the schedule for the talks, as well as the homework assignments.| Date | Lecturer | Subject | ||
|---|---|---|---|---|
| 10 Feb 2023 | Jan Vonk | Motivation and overview / Valued fields | ||
| - | No problem class | |||
| Homework: Choose two exercises from 1.8 - 1.17 | ||||
| 17 Feb 2022 | Jan Vonk | Complete fields | ||
| Mike Daas | Exercises chapter 1. | |||
| Homework: Choose one exercise from 1.18 - 1.20 and one from 2.7 - 2.13 | ||||
| 24 Feb 2022 | Jan Vonk | Local fields and Hensel's Lemma | ||
| Mike Daas | Exercises chapter 1/2. | |||
| Homework: Choose two exercises from 2.14 - 2.23 | ||||
| 3 Mar 2022 | Eugenia Rosu | Extensions of valuations | ||
| Mike Daas | Exercises chapter 2. | |||
| Homework: TBA | ||||
| 10 Mar 2023 | - | (Vrije week) | ||
| - | - | |||
| - | ||||
| 17 Mar 2022 | Eugenia Rosu | Extensions of complete fields | ||
| Mike Daas | Exercises chapter 3. | |||
| Homework: Choose one problem from 3.14 - 3.19 and one problem from 4.1 - 4.5 | ||||
| 24 Mar 2023 | Marco Streng | Galois theory of valued fields | ||
| Mike Daas | Exercises chapter 4. | |||
| Homework: Choose two problems from 4.6 - 4.16 | ||||
| 31 Mar 2023 | Eugenia Rosu | Galois theory of valued fields | ||
| Mike Daas | Exercises chapter 5. | |||
| Homework: Choose two problems from 5.1 - 5.11 | ||||
| 7 Apr 2023 | - | (Goede vrijdag) | ||
| - | - | |||
| - | ||||
| 14 Apr 2023 | Eugenia Rosu | The Kronecker-Weber theorem | ||
| Mike Daas | Exercises chapter 5. | |||
| Homework: Choose one problem from 5.12 - 5.15 and one from 6.1 - 6.6. | ||||
| 21 Apr 2023 | Jan Vonk | Adèles and idèles, global class field theory | ||
| Mike Daas | Exercises chapter 5/6. | |||
| Homework: None. | ||||
| 28 Apr 2023 | Jan Vonk | Ring class fields and primes of the form x2+ny2 | ||
| Mike Daas | Exercises ring class fields. | |||
| Homework: Primes of the form x2+ny2 for your favourite n. | ||||
| 5 May 2023 | - | (Bevrijdingsdag) | ||
| - | - | |||
| - | ||||
| 19 May 2023 | - | (Hemelvaart brug) | ||
| - | - | |||
| - | ||||
| 23 May 2023 | Jan Vonk | The theory of complex multiplication (!SNELLIUS 403, 10am) | ||
| Jan Vonk | Q&A session (!SNELLIUS 403) | |||
| - | ||||
| 26 May 2023 | Eugenia Rosu | Tate's thesis | ||
| Mike Daas | ||||
| Homework: TBA | ||||
| 2 June 2023 | Eugenia Rosu | Tate's thesis | ||
| Mike Daas | ||||
| Homework: TBA | ||||
