2008 Fiscal Year Final Research Report
The arithmetic of abelian varieties with complex multiplication and Euler systems.
| Project/Area Number |
19740010
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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 | Keio University (2008-2009)
Nagoya University (2007) |
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Principal Investigator |
BANNAI Kenichi Keio University, 理工学部, 講師 (90343201)
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| Co-Investigator(Renkei-kenkyūsha) |
KOBAYASHI Shinichi 東北大学, 大学院・理学研究科, 准教授 (80362226)
TSUJI Takeshi 東京大学, 大学院・数理科学研究科, 准教授 (40252530)
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| Research Collaborator |
GUIDO Kings Regensburg University (Germany), Professor
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| Project Period (FY) |
2007 – 2008
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| Keywords | ポリログ / 楕円曲線 / アーベル多様体 |
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| Research Abstract |
In this research, we investigated motivic objects such as the polylogarithm and the Eisenstein classes, for the case of elliptic curves, which are one dimensional abelian varieties. We have obtained the following results. Through joint research with Shinichi Kobayashi and Takeshi Tsuji, we gave an explicit description of the p-adic realization of the elliptic polylogarithm for a prime p≧5, even in the case when the elliptic curve has complex multiplication and good supersingular reduction at p, for the Frobenius lifting which is the second power of the absolute Frobenius. Also, through joint research with G. Kings, we gave an explicit description of the p-adic Eisenstein class on the modular curve when p≧5 is a prime of good ordinary reduction.
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