2011 Fiscal Year Final Research Report
P-adic L-function and P-adic Beilinson conjecture
| Project/Area Number |
21740009
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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 | Tohoku University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | ゼータ関数 / 岩澤理論 / p-進L-関数 / p進Beilinson予想 / Birch and Swinnerton-Dyer予想 / 楕円曲線 / 整数論 |
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| Research Abstract |
I studied the p-adic L-function of elliptic curves defined over the rational number field. I obtained the p-adic Gross-Zagier formula at supersingular prime p that describes the derivative of the p-adic L-function of elliptic curves base changed over an imaginary quadratic field satisfying the Heegner condition in terms of the p-adic height of the Heegner point. As an application, I proved the full Birch and Swinnerton-Dyer conjecture for CM elliptic curves of rank 1 up to bad primes. This formula also gives an important example of the p-adic Beilinson conjecture.
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