Talk given on Tuesday January 24th 2006 in the Institute for Experimental Mathematics (IEM).

 

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This talk was given on Winter semester 2005/06 in the University of Duisburg-Essen, Campus Essen. It follows a talk given by Xavier Taixes as a part of a seminar on Galois Representations in Modular Forms.

We study modular forms and Galois representations over finite and fields and over the complex numbers. We give the proof of an important theorem from Serre and Deligne that in every modular form of weight 1 we can attach a linear representation. This representation is unique up to isomorphism. During the seminar we already saw that this theorem holds for arbitrary weight.

Organisation: G. Boeckle, G. Frey, M. Moeller.

 

The program of the seminar:

 

18.10.05	1. Introduction (Organizational)	Gebhard Boeckle
25.10.05	2. Eisher-Shimura Isomprhisms: Statement	Jan Christian Rohde
08.11.05	3. Eisher-Shimura Isomprhisms as Hodge structure	Kay Ruelling
??.11.05	4. Intermezzo: Variation of the Hodge structure over Hilbertian module variaties	Eckart Viehweg
15.11.05	5. Γ1(N) and Modulschemes for elliptic curves	Oscar Ledesma
22.11.05	6. Hecke operators, classic and geometric	Phung Ho Hai
29.11.05	7. Hecke algebra, Peterson's scalar product, Newforms	Bjoern Buth
06.12.05	8. Weight 2, part 1	Stefan Kukulies
13.12.05	9. Weight 2, part 2: The Eisher-Shimura relations	Jochen Heinloth
20.12.05	10. Arithmetic Modules for Modular curves	Irene Bouw
10.01.06	11. Etale Cohology and the theorem for weight > 1	Marco Wolter
17.01.06	12. Weight 1 (part 1)	Xavier Taixes
24.01.06	13. Weight 1 (part 2)	Marios Magioladitis
03.02.06	14. Overview to "applications"	Gerhard Frey

Program in German: [pdf]

References

1. Deligne, P. Serre, J.-P., Formes modulaires de poids 1, Ann. Sci. ENS. 7 No.4 (1974), 507-530

2. G. Frey (ed.), On Artin's conjecture for odd 2-dimensional representations, Lecture notes in math. 1585 (1994), Springer-Verlag.

 

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Last update: February 4th, 2006