Number theory days

Session

Galois representations and modular forms

Jun 24, 2014, 9:00 AM

Salle de réunions (Université Lille 1)

Conveners

Galois representations and modular forms

• Mladen Dimitrov (Université Lille 1)

6. Rings and images occurring from universal deformations of profinite groups

Gebhard Boeckle (Heidelberg University)

6/24/14, 9:00 AM

Galois representations and modular forms

Recently Dorobisz, Eardley-Manoharmayum and Manoharmayum have proved abstract results (a) on the shape of possible deformation rings and (b) on the image of universal deformations of profinite groups, for representations into GL_n. The result regarding (a) were motivated by questions of Bleher, Chinburg and de Smit. We place these results in an axiomatic framework that in principle applies to...

20. Equivariant L-values of modular abelian varieties

François Brunault (École normale supérieure de Lyon)

6/24/14, 10:30 AM

Galois representations and modular forms

An abelian variety defined over a number field is called strongly modular when its L-function is the product of L-functions of modular forms of weight 2. In this talk, we will show a weak version of Beilinson's conjectures for non-critical L-values of strongly modular abelian varieties. We will explain the interest of formulating an equivariant version of these conjectures (after Burns and...

5. On the modularity of reducible mod l Galois representations

Nicolas Billerey (Université Clermont-Ferrand 2)

6/24/14, 11:45 AM

Galois representations and modular forms

In this talk, I'll give a modularity result for reducible mod l Galois representations. By analogy with the irreducible case, I'll state some questions regarding characterization and optimization of the different types of modular forms attached to such a given representation. Finally, I'll give an application of these results to the determination of an explicit lower bound for the highest...

7. The future of modularity

Luis Dieulefait (Universitat de Barcelona)

6/24/14, 3:30 PM

Galois representations and modular forms

This is joint work with Ariel Pacetti. We present generalizations to totally real number fields of the construction done by the speaker some years ago over Q that allows to connect to each other any given pair of newforms through chains of modular compatible systems of Galois representations. We also discuss applications of this, and we consider the case of abstract Galois representations and...

8. Automorphic Galois representations in the inverse Galois problem

Gabor Wiese (Université du Luxembourg)

6/24/14, 5:00 PM

Galois representations and modular forms

In the talk I will report on recent results on the inverse Galois problem based on compatible systems of Galois representations coming from modular and automorphic forms. The focus will be on ideas and strategies as well as the obstacles that are preventing us from proving much stronger theorems. In this context, the role of coefficient fields will be particularly highlighted. Most parts are...