Study on Iwasawa theoretic phenomena appearing in non-commutative Galois deformations

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800014
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Algebra
• Research Institution: Tokyo Denki University
• Principal Investigator: HARA Takashi 東京電機大学, 未来科学部, 助教 (40722608)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 非可換岩澤理論 / 岩澤主予想 / p進L関数 / セルマー群 / CM体 / 虚数乗法 / 肥田変形 / ガロワ変形

Outline of Final Research Achievements

In this research, we studied mainly (1) Iwasawa main conjecture for nearly ordinary Hilbert cusp forms with complex multiplication (joint with Tadashi Ochiai), (2) Noncommutative Iwasawa theory for CM number fields. For (1), we established a reduction technique to deduce the cyclotomic Iwasawa main conjecture for Hilbert cuspforms with complex multiplication from the multivariable main conjecture for CM fields (the paper is now accepted and published). We are now planning to extend our result to the main conjecture of nearly ordinary Hilbert Hida families. For (2), we succeeded to describe conditions to patch the multivariable p-adic L-functions for CM number fields in several easy cases. We are now trying to extend our result to rather general extensions of CM fields, and we hope to complete the first draft of the paper soon.

Free Research Field

整数論・数論幾何学