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 |
Research Field |
Algebra
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Research Institution | Tsuda College |
Principal Investigator |
MATSUNO KAZUO 津田塾大学, 学芸学部, 准教授 (40332936)
|
Project Period (FY) |
2010-04-01 – 2014-03-31
|
Project Status |
Completed (Fiscal Year 2013)
|
Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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Keywords | 整数論 / 楕円曲線 / Tate-Shafarevich群 / 代数学 / 岩澤理論 |
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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Report
(5 results)
Research Products
(8 results)