On various generalizations of Iwasawa theory
| Project/Area Number |
20740013
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | モジュラーシンボル / P進L関数 / 肥田理論 / 岩澤理論 / ヒルベルトモジュラー形式 / ジーゲルモジュラー形式 / セルマー群 / オイラー系 / Euler系 / ガロア表現 / 高次元モジュラーシンボル / p進L函数 / Bertiniの定理 / 肥田変形 |
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| Research Abstract |
We obtained several results on generalized Iwasawa theory especially on the function-field analogue of Iwasawa theory studying abelian varieties over global fields of positive characteristic and the deformation-theoretic generalization of Iwasawa theory. For the algebraic side of Iwasawa theory, we proved the control theorem to study the behavior of Selmer groups on Hida deformations of Hilbert modular forms. For the analytic side of the theory, we constructed the p-adic L-functions in several variables on Hida deformations of Hilbert modular forms. We also worked on the Hida deformations of Siegel modular forms. We constructed the Coleman. Perrin-Riou map which interpolates dual exponential maps on the deformation. We also generalized our result on Euler system for deformation spaces removing the assumption that the deformation ring is regular.
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Report
(6 results)
Research Products
(41 results)
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[Journal Article] Fabien Trihan2009
Author(s)
Tadashi Ochiai
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Journal Title
On the Selmer groups of abelian varieties over function fields of characteristic p Mathematical Proceedings of the Cambridge Philosophical Society 146, No.1
Pages: 23-43
Related Report
Peer Reviewed
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