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modularity of elliptic curves over some totally real fields

Hold Date 2016-11-04 16:00~2016-11-04 17:00

Place Lecture Room M W1-C-512, West Zone 1, Ito campus, Kyushu University

Object person  

Speaker Sho YOSHIKAWA (Graduate School of Mathematical Sciences, The University of Tokyo)

The classical Shimura-Taniyama conjecture states that any elliptic curve over the field of  rational numbers is modular. This conjecture is now a theorem by the works of Wiles, Taylor-Wiles, and Breuil-Conrad-Diamond-Taylor. Recently, progress in modularity lifting theorem has made it possible to prove various results on a natural generalization of the Shimura-Taniyama conjecture to the totally real field cases. In this talk, I will explain my recent result on modularity of all elliptic curves over abelian totally real fields unramified in 3,5, and 7.

* This seminar is combined with Algebra Seminar.