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Abstracts for 36th Seminar Aachen-Köln-Lille-Siegen on Automorphic Forms

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Mathieu Moonshine

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Speaker: 
Matthias Gaberdiel
Affiliation: 
ETH Zürich
Date: 
Wed, 20/06/2012 - 14:00 - 14:50
Location: 
MPIM Lecture Hall
Parent event: 
36th Seminar Aachen-Köln-Lille-Siegen on Automorphic Forms

Some examples of abelian surfaces with everywhere good reduction

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Speaker: 
Lassina Dembélé
Affiliation: 
University of Warwick/MPI Bonn
Date: 
Wed, 20/06/2012 - 15:00 - 15:50
Location: 
MPIM Lecture Hall
Parent event: 
36th Seminar Aachen-Köln-Lille-Siegen on Automorphic Forms

A celebrated result of Fontaine dated 1981 shows that there is no
abelian scheme over Z. In other words, there is no abelian variety over
Q with everywhere good reduction. This result is no longer true over
general number fields. In fact, long before Fontaine's result, Tate showed

Arithmetic properties of automorphic $L$-functions

Posted in
Speaker: 
Anantharam Raghuram
Affiliation: 
Oklahoma State University/MPI Bonn
Date: 
Wed, 20/06/2012 - 17:00 - 17:50
Location: 
MPIM Lecture Hall
Parent event: 
36th Seminar Aachen-Köln-Lille-Siegen on Automorphic Forms

In the first part of the talk, I will discuss the example of critical values for $L$-functions for $GL(2)$ in some detail. This part is an exposition, in the framework of automorphic representations, of the classical results of Manin, Shimura, etc. In the latter part, I will sketch results of my work, which is partly in separate collaborations with Grobner, Harder and Shahidi, on the special values for automorphic $L$-functions for higher $GL(n)$.

 

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