Study on Iwasawa theoretic phenomena appearing in non-commutative Galois deformations
| 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
|
| Project Status |
Completed (Fiscal Year 2017)
|
| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
|---|
| 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 / ヒルベルト保型形式 / 非可換p進ゼータ関数 / 捩れ合同式 / CM体の岩澤理論 / 高次Fitting不変量 / 概通常ヒルベルト肥田族 / 整数論 / 数論幾何学 / 岩澤理論 / ガロワ表現 / オイラー系 / 保型形式 |
|---|
| 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.
|
Report
(5 results)
Research Products
(13 results)
