Research on the equivariant Tamagawa number conjecture and higher rank Iwasawa theory
| Project/Area Number |
17K14171
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka City University |
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Principal Investigator |
Sano Takamichi 大阪市立大学, 大学院理学研究科, 准教授 (30794698)
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | オイラー系 / 岩澤主予想 / 玉河数予想 / 楕円曲線 / ゼータ元 / モチーフ / Heegner点 / 同変玉河数予想 / 非可換 / コリヴァギン系 / Rubin-Stark元 / Perrin-Riou予想 / スターク系 / 岩澤理論 / ルービン・スターク元 / スターク予想 |
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| Outline of Final Research Achievements |
We succeeded in establishing the theory of Euler-Kolyvagin systems and gave a partial solution to higher rank Iwasawa main conjectures as an application of our theory. Furthermore, we formulated an Iwasawa main conjecture for a general motive and gave a strategy for solving the Tamagawa number conjecture. We particularly studied Kato's Euler system for elliptic curves in detail and gave a partial solution to the Mazur-Tate conjecture. We also gave a natural strategy for solving the Birch-Swinnerton-Dyer conjecture. Lastly, we gave analogous results for the Heegner point Euler system.
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| Academic Significance and Societal Importance of the Research Achievements |
高階オイラー・コリヴァギン系の理論を構築し、Mazur-Rubin予想を解決した。これは新しい理論を作り上げた点と、未解決予想を解決したという点で学術的意義がある。さらに、Mazur-Tate-Teitelbaum予想やMazur-Tate予想といった予想を一般のモチーフに対する一つの予想から導き、別個の現象を一つの現象から統一的に解釈したという点で意義がある。
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Report
(6 results)
Research Products
(24 results)
