数論幾何学セミナー「The modular form method in Iwasawa theory」

開催日時
2014年   10月 16日 10時 00分 ~ 2014年   10月 17日 16時 00分
場所
北海道大学理学部3号館210
講演者
萩原 啓 (北海道大学)
 
Abstract: In 1970s, Ribet invented an elegant method for the construction
of suitable unramified extensions of number fields using modular forms,
giving a proof of the converse of Herbrand's theorem.

His ingenious method (the modular form method) has become one of the two
main techniques in Iwasawa theory along with the Euler system method, as
is seen from the proof of the Iwasawa main conjecture due to Mazur-Wiles
and the recent achivement of Skinner-Urban in Iwasawa theory for GL_2.

In this talk, we give the central ideas in this method through the
explanation of

- Ribet's proof of the converse of Herbrand's theorem, and

- Wiles's approach to the Iwasawa main conjecture over the rational field
using the Hida family of elliptic modular forms.


関連項目

研究集会・セミナー・集中講義の一覧へ