Number Theory Seminar on Modular Curves
Description
We are starting a working seminar on rational points of modular curves. We plan to cover the following topics:
1. Introduction to schemes and group schemes
2. The Neron model of an abelian variety
3. Introduction to modular curves
4. Characterization of modular curves as moduli spaces of elliptic curves with additional structure, their relation with Serre's Open Image Theorem and with solving diophantine equations
5. Rational points on X_0(N): Mazur's work
6. Mestre's graph method
7. The winding quotient of an abelian variety: Merel's work
8. Heegner points
9. Rational points on X_split(N): work of Momose and Parent
10. Special values of L-functions: work of Gross and Gross-Kudla
If you are interested in giving a talk, please contact Prof. A.C. Cojocaru at:
Schedule
| 10:00 to 11:00 |
Modular curves as moduli spaces
Reinier Broker |
| 13:00 to 14:30 |
Modular curves as moduli spaces and diophantine applications
Reinier Broker |
| 13:30 to 15:00 |
Introduction to modular curves
Roger Oyono |
| 13:00 to 15:00 |
The Neron model of an abelian variety
Elisa Gorla, University of Neuchatel |
| 11:00 to 12:00 |
An introduction to schemes and group schemes
Elisa Gorla, University of Neuchatel |
