The goal of the seminar is to obtain a thorough understanding of quaternion algebras and to get an idea about the construction of the Galois representation attached to a Hilbert modular form.
In the beginning the arithmetic theory of quaternion algebras will be introduced in detail and will be illustrated by many examples. Then Shimura varieties attached to quaternion algebras will be studied, as well as automorphic forms on them. Hilbert modular forms will be introduced and the Jacquet-Langlands correspondence will be stated. The final lecture will sketch the construction of the Galois representation attached to a Hilbert modular eigenform.
Gebhard Böckle, Juan Marcos Cerviño, Lassina Dembélé, Gerhard Frey, Gabor Wiese
Here is the final version of the programme.
|1||10/04/2008||Ambrus Pal|| Guest lecture:|
The Manin constant of elliptic curves over function fields
|2||17/04/2008||Marc-Hubert Nicole|| Guest lecture: |
Superspecial abelian varieties and their quaternion orders
[Marc-Hubert's lecture notes]
|3||24/04/2008||Marco Wolter|| Quaternion algebras over fields |
[Marco's lecture notes]
|4||08/05/2008||Marios Magioladitis|| Arithmetic of quaternion algebras: orders and ideals |
[Marios' lecture notes]
|5||15/05/2008||Adam Mohamed||Quaternion algebras over local fields|
|6||29/05/2008||Eduardo Ocampo|| Quaternion algebras over global fields |
[Eduardo's lecture notes]
|7||05/06/2008||Björn Buth||Arithmetic of quaternion algebras over global fields|
|8||12/06/2008||Ralf Butenuth|| Trace formula and Brandt matrices |
[Ralf's lecture notes]
|9||19/06/2008||Oscar Ledesma||Shimura Curves I|
|10||26/06/2008||Stefan Kukulies|| Shimura Curves II |
[Stefan's lecture notes]
|11||03/07/2008||Phùng Hô Hai||Hilbert Modular Forms|
|12||10/07/2008||Kay Rülling|| Shimura Curves III |
[Kay's lecture notes]
|13||17/07/2008||Gabor Wiese|| The Galois Representation Attached to a Hilbert Modular Form|
[Gabor's lecture notes]
Last modification: 4 September 2008.