Seminar on Arithmetic Algebraic Geometry [The modular form method in Iwasawa theory」
 Date

20141016 10:00 
20141017 16:00
 Place
 Faculty of Science Bld. No.3210

Speaker/Organizer
 Kei Hagihara (Hokkaido University)

 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 MazurWiles
and the recent achivement of SkinnerUrban 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.