Séminaires : Séminaire Théorie des Nombres

Equipe(s) : fa, tn, tga,
Responsables :Marc Hindry, Bruno Kahn, Wieslawa Niziol, Cathy Swaenepoel
Email des responsables : cathy.swaenepoel@imj-prg.fr
Salle :
Adresse :



Orateur(s) K. Buzzard - ,
Titre Level-lowering for mod 2 modular forms.
Horaire15:30 à 17:30
RésumeIn 1985, Ken Ribet proved a "level-lowering" theorem in the theoryof mod p modular forms, valid for forms of level Gamma_0(N) andprimes p>2. As a consequence of this result he was able to provethat the Taniyama-Shimura conjecture implied Fermat's Last Theorem.Wiles also used this level-lowering theorem in his initial proof ofthe semi-stable Taniyama-Shimura conjecture.Taylor's approach to settling infinitely many new cases of aconjecture of Artin was based on these ideas of Wiles and Ribet, butunfortunately he needed to work with p=2, where Ribet's work, as itstood, did not apply. I will explain Taylor's approach, how oneproves level-lowering for p=2, and what the consequences are for thisconjecture of Artin.