6 EC
Semester 2, period 4, 5
5334TINT6Y
In this coure we will study class field theory. Class field theory describes the algebraic structure of abelian extensions of global fields, such as number fields (finite algebraic extensions of the rational numbers) and function fields (finite algebraic extensions of the field of rational functions).
In particular one of the goals of the course is to discuss and prove (as much as we can of) the fundamental theorems of class field theory, including the existence of abelian extensions and the isomorphism between the class group and the Galois group of the class field. We will also discuss Chebotarev density theorem, cohomology of groups, local class field theory, and (if time permits) ideles and adeles.
Throughout the course, we will consider various examples and applications to illustrate the concepts and techniques introduced.
Prerequisites for this course include a strong background in abstract algebra and algebraic number theory. Familiarity with Galois theory and algebraic geometry may also be helpful, but is not strictly necessary.
Finally, the course will also feature a computer algebra component at the end.
Students will need their own laptops to participate in the lab sessions.
Classes will involve lectures covering the basic theory, including examples and applications. Students will spend self-study time on problem sheets designed to test and enhance their understanding of the course material. These will then be discussed during class. Familiarity with computer algebra packages will be developed during two computer lab sessions, led by Prof. Dokchitser.
|
Activity |
Hours |
|
|
Hoorcollege |
22 |
|
|
Computational aspects sessions |
8 |
|
|
Tentamen |
3 |
|
|
Self study |
135 |
|
|
Total |
168 |
(6 EC x 28 uur) |
This programme does not have requirements concerning attendance (TER-B).
Additional requirements for this course:
Students should inform the course coordinator of any absence.
| Item and weight | Details |
|
Final grade | |
|
1 (100%) Tentamen |
The exam will be a written exam with no calculator or notes allowed. Students are required to obtain a minimum of 5 on the final exam involve pass the course. Any homework assignment handed in more than a week late will receive no marks. The computational assignment will need to be handed in at the final class of the semester (13/5).
Grades for the computational assignment can be discussed during office hours that will be communicated to the students in class.
After the two computer lab sessions the students will be given an assignment that they are expected to complete by the end of the course, to be handed in at the final class.
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl
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The schedule for this course is published on DataNose.