| Project/Area Number |
20540004
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tohoku University |
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Principal Investigator |
NAKAMURA Tetsuo Tohoku University, 理工学術院, 教授 (90016147)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Atsusi 東北大学, 大学院・理学研究科, 助教 (30241516)
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| Co-Investigator(Renkei-kenkyūsha) |
TERAI Nobuhiro 足利工業大学, 準教授 (00236978)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
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: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | 楕円曲線 / 虚数乗法 / アーベル多様体 / トーション / 類数 / 整数点 / モルデル・ヴェイユ群 / 代数体 / アーベル曲面 / Mordell-weil群 / 有理点 |
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| Research Abstract |
To determine the structure of torsion groups of abelian varieties defined over the rationals is an important problem in number theory. The case of dimension one is already settled. In our research we investigated the case of dimension two, non simple and of CM type. We determined the orders of torsion elements of such abelian surfaces.
Using rational points of elliptic curves we constructed an infinite number of number fields whose class numbers are divisible by a certain integer.
For a special class of elliptic curves, we gave concretely integer points and generators of Mordell-Weil groups.
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