Institute of Mathematics for Industry

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On non-commutative Iwasawa theory for CM number fields


Hold Date 2018-07-20 16:00~2018-07-20 17:00

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

Object person  

Speaker Takashi HARA (Tokyo Denki University)

Abstract:
I will explain my recent approach to non-commutative Iwasawa theory for CM number fields. Firstly I apply the framework of Jürgen Ritter and Alfred Weiss's equivariant Iwasawa theory to CM number fields, and propose the non-commutative Iwasawa main conjecture so that it would be a natural extension of the (classical) multivariable Iwasawa main conjecture for CM number fields. Then I will report, comparing the situation to the case of totally real number fields, a current status upon the algebraic side of the argument towards the proof of the main conjecture (that is, deduction of ``the gluing conditions'' for the p-adic zeta functions associated to intermediate abelian extensions). If time permits, I would like to state future perspective concerning the analytic side of the argument (verification of ``the gluing conditions'') after introducing previous related results due to Athanasios Bouganis and Dohyeong Kim.