Seminars

Eisenstein primes at composite level

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Kenneth A. Ribet

2014-08-04
15:00:00 - 16:00:00

R202 , Astronomy and Mathematics Building



Before my lecture Taiwan University, I will have described some work by me and by Hwajong Yoo at the NCTS Conference on the Impact of Computation on Number Theory. This work concerns Eisenstein primes, maximal ideals in Hecke algebras for which the associated two-dimensional Galois representations are reducible. After reviewing the relevant definitions and giving an overview of our work, I will focus on questions that did not arise in my lecture at NCTS. Most likely, I will explain what is known about the dimension of the kernel of an Eisenstein prime on the Jacobian of the associated modular curve.

※Professor Ribet is world’s leading expert on algebraic number theory. He is a member of the National Academy of Sciences of USA, and has received the Fermat Prize in 1989. He proved in late 1980’s that the Fermat’s last theorem would follow from the Taniyama-Shimura conjecture. This great theorem paves the way towards Wiles's later successful proof of Fermat's last theorem.