6 EC
Semester 2, period 4, 5
5334TINT6Y
| Owner | Master Mathematics |
| Coordinator | dr. A.L. Kret |
| Part of | Master Mathematics, |
This course will be an introduction to Galois representations. We will first consider the absolute Galois group G_K of a number field K, and study various structures defined on it (Frobenius elements, decomposition groups, ramification filtration, complex conjugations, etc).
After this we will look at various categories of representations of G_K. In particular we will look at Artin representations (those representations with finite image).
There will also be computer lab sessions involving explicit and computational aspects.
Students wishing to attend this course will need to have attended the Algebraic Number Theory Mastermath course in the first semester, or to have a good understanding of the contents of this course. Algebraic geometry 1 is also recommended, but not required.
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).
Weekly homework problems will be returned to students and can be discussed in class, after they have been marked. Grades for the computational assignment can be discussed during office hours that will be communicated to the students in class.
There will be problem sheets, which the students are expected to complete in their own time. These will be discussed at the start of the next class. In the final exam, some of these problems will reappear.
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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| 16 |
The schedule for this course is published on DataNose.