Course manual 2025/2026

Course content


In this course we will study Galois representations. We will first introduce and study the absolute Galois group of a number field. After this we will look at various ways to contstruct representations of it, such as via the Tate module of an elliptic curve. If time and background of the audience permits, we will also look at etale cohomology.  

Prerequisites for this course include a strong background in abstract algebra and algebraic number theory. Familiarity with Galois theory, representation theory and algebraic geometry may also be helpful, but is not strictly necessary.

 

Study materials

Literature

  • Course notes

Objectives

    Teaching methods

    • Lecture
    • Self-study

    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.

    Learning activities

    Activity

    Hours

     

    Hoorcollege

    22

     

    Computational aspects sessions

    8

     

    Tentamen

    3

     

    Self study

    135

     

    Total

    168

    (6 EC x 28 uur)

    Attendance

    This programme does not have requirements concerning attendance (TER-B).

    Additional requirements for this course:

    Students should inform the course coordinator of any absence.

    Assessment

    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).

    Inspection of assessed work

    Grades for the computational assignment can be discussed during office hours that will be communicated to the students in class.

    Assignments

    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.

    Fraud and plagiarism

    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

    Course structure

    WeeknummerOnderwerpenStudiestof
    1
    2
    3
    4
    5
    6
    7
    8
    9
    10
    11
    12
    13
    14
    15
    16

    Contact information

    Coordinator

    • Arno Kret