2018-2019 : Étale cohomology (M2)
Here are the course notes.
2018-2019 : Riemann surfaces (M1)
Voir la page dédiée sur le portail des études de l'ENS Lyon. Les TD sont assurés par Bruno Sévennec.
In this course, we will cover the following topics:
- Definition of Riemann surfaces and holomorphic maps.
- Examples: the Riemann sphere, complex tori, elliptic functions.
- The identity theorem. Applications: discreteness of the fibers, open mapping theorem.
- Holomorphic maps between compact Riemann surfaces, ramification theory.
- Meromorphic functions with prescribed zeros and poles.
- Holomorphic differential forms, residues, genus of a compact Riemann surface.
- Quotients of Riemann surfaces. Statement of the uniformization theorem.
- Some examples of modular curves.
- Examples of monodromy representations.
- TD 1
- TD 2
- TD 3
- TD 4 - Solution Exercise 2
- TD 5 - Solution Exercise 3
- TD 6 - Solution Exercise 2
- TD 7
- TD 8 - Solution Exercise 1, Exercise 2
- TD 9
- TD 10 - Solution Exercise 1
- TD 11
2018-2019 : Option C (Agrégation)
La préparation à l'option C est assurée en commun avec Auguste Hébert.
