2013 Fiscal Year Final Research Report
Development of an algorithm for the calculation of the Tate-Shafarevich groups and applicaiton
| Project/Area Number |
22740024
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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 | Tsuda College |
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Principal Investigator |
MATSUNO KAZUO 津田塾大学, 学芸学部, 准教授 (40332936)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 整数論 / 楕円曲線 / Tate-Shafarevich群 |
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| Research Abstract |
We develop an algorithm for the calculation of the Tate-Shafarevich groups of elliptic curves defined over number fields. We also make a numerical verification of a conjecture by Greenberg for 2-adic Iwasawa mu-invariants of elliptic curves and 2-adic Iwasawa main conjecture for elliptic curves by using a relation between mu-invariants of elliptic curves and partly ramified Iwasawa modules associated with certain number fields. Moreoer, we find some examples related to the problem about the rank of the Mordell-Weil group of elliptic curves over number fields.
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