Sommersemester 2008 - Forschungsseminar on Quaternion Algebras


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.

List of Lectures

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 Phng H 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.