Présidents de session
Représentations galoisiennes et formes modulaires
- Mladen Dimitrov (Université Lille 1)
Gebhard Boeckle
(Heidelberg University)
24/06/2014 09:00
Représentations galoisiennes et formes modulaires
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...
François Brunault
(École normale supérieure de Lyon)
24/06/2014 10:30
Représentations galoisiennes et formes modulaires
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...
Nicolas Billerey
(Université Clermont-Ferrand 2)
24/06/2014 11:45
Représentations galoisiennes et formes modulaires
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...
Luis Dieulefait
(Universitat de Barcelona)
24/06/2014 15:30
Représentations galoisiennes et formes modulaires
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...
Gabor Wiese
(Université du Luxembourg)
24/06/2014 17:00
Représentations galoisiennes et formes modulaires
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...
