## Sommersemester 2008 - Forschungsseminar on Quaternion Algebras

- Date: Thursday, 10-12 a.m.
- Place: The first session will take place in the lecture room on the
fourth floor at the University.
- Starting date: 10 April 2008
- The language of the seminar will be English.
- Log on.

### Description

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.

### Organisers

Gebhard Böckle, Juan Marcos Cerviño,
Lassina Dembélé, Gerhard Frey, Gabor Wiese

### Programme

Here is the final version of the programme.

### List of Lectures

| **Date** | **Speaker** | **Title** |

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.