Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
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http://www.imj-prg.fr/tn/STN/stnj.html

 


Orateur(s) K. Buzzard - ,
Titre Level-lowering for mod 2 modular forms.
Date15/05/2000
Horaire15:30 à 17:30
Diffusion
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.
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