Algebra V - Galois theory

Instructor: Aline Zanardini <aline.zanardini@epfl.ch>

Assistant:  Raymond Cheng <raymond.cheng@epfl.ch>

Course: Thursday, 10.15-12:00, MA A1 10
Exercises: Thursday, 13:15-15:00, GC B3 30

The course and exercises will be given in English.

The first lecture is on Thursday, 11/09, at 10h15 in MA A1 10. It will consist of an overview of the course and a discussion of formalities, followed by an exposition of problems that inspired the development of Galois Theory.

The first exercise class is on Thursday, 11/09, at 13h15 in GC B3 30. 

I am looking forward to teaching this class, and I hope that we will all have some fun this semester.

The second lecture will recall algebraic extensions, splitting fields, and algebraic closures.

Important: This week there will be no exercise session. Instead, we will have two lectures.

We will recall normal and separable extensions. We will also start our discussion on Galois extensions and the Galois correspondence.

Important: This week there will be no lecture. Instead, you will have two exercise sessions.

We will start a discussion on cyclic and cyclotomic field extensions.

This week, Raymond gives the lecture and the exercises session.

The topic will be (Abelian) Kummer extensions.

This week, I (Aline) will also hold the exercises session.

This week, Raymond gives the lecture and the exercises session.

We will start a discussion on Galois cohomology.

• We continue with our discussion on Galois cohomology.
• We discuss an "application" of Galois cohomology.
• We give a short introduction to the inverse Galois problem.
• We discuss cubics and quartics.
• Computing the Galois group.

• Proof of Hilbert's irreducibility theorem (non-examinable).

• Infinite Galois extensions (non-examinable).

• Review session