Algebra V - Galois theory

Instructor: aline.zanardini@epfl.ch

Assistant:  emre.ozavci@epfl.ch

Course: Wednesday, 13.15-15:00, MA A110

Exercises: Friday, 15:15-17:00, MA A112

The course and exercises will be given in English.

The first lecture is on Wednesday, 11/09, at 13h15 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 Friday, 13/09, at 15h15 in MA A1 12. 

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

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

The third lecture will recall normal and separable extensions.

We will start our discussion on Galois extensions and the Galois correspondence.

Here are two suggestions for further reading with many examples:

• These and these notes by Keith Conrad.

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

This week, there will be two exercise sessions (no lecture).

• One will be during lecture time on Wednesday, October 30 (in MA A1 10, usual time 13:15-15:00).
• Another one is the usual day, time, and place.

This week, there will be two lectures (no exercise session).

• One the usual day of the week, time, and place.
• Another is when (15:15-17:00) and where (MA A1 12) you usually have the exercise session on Fridays.

We will start a discussion on Galois cohomology.

• An "application" of Galois cohomology.
• A short introduction to the inverse Galois problem.
• Cubics and quartics.

• Computing the Galois group.

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

• Infinite Galois extensions (non-examinable).
• IMPORTANT: On Friday, December 20, there will be a make-up class instead of the exercise session. It will be a review session.
• On Dec 20, we will meet from 15:15-17:00 in MA A1 12.