Quid of Hilbert class field tower and ramification of prime ideals

par Marie Gros (Institute de Mathematiques de Toulouse)

mercredi 4 nov. 2026, 18:00 → 19:30 Europe/Paris

207 (Salle Pellos) (1R2)

The goal of this talk is to have a peak at the class field tower problem. For this, we will have to understand the concept involved. In the context of a number field (finite field extension of Q), I will give meaning to prime ideal and look at what happens to a prime ideal when we take a field extension. This will allow us to introduce the concept of ramification and inertia and give us the pleasure of using a little bit of Galois theory. From there, I will be able to define the class group of a number field, and reach the goal of the definition of the Hilbert class field tower.