| Project/Area Number |
60540035
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
代数学・幾何学
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| Research Institution | NAGOYA INSTITUT OF TECHNOLOGY |
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Principal Investigator |
MIWA Megumu NAGOYA INSTITUT OF TECHNOLOGY, 工学部, 教授 (30011521)
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| Co-Investigator(Kenkyū-buntansha) |
WATANABE Keiichi NAGOYA INSTITUT OF TECHNOLOGY, 工学部, 助教授 (10087083)
TAKEMOTO Fumio NAGOYA INSTITUT OF TECHNOLOGY, 工学部, 助教授 (50022645)
KATO Akikuni NAGOYA INSTITUT OF TECHNOLOGY, 工学部, 助教授 (20024226)
SHIMIZU Akinobu NAGOYA INSTITUT OF TECHNOLOGY, 工学部, 助教授 (10015547)
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| Project Period (FY) |
1985 – 1986
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| Project Status |
Completed (Fiscal Year 1986)
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| Budget Amount *help |
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1986: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 1985: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | 楕円曲線のMordell-Weil群の階数について |
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| Research Abstract |
The Mordell-Weil group of elliptic curve itself is not only a very interessting theme of mathematical research but also a very important one in connection with number theory especially arithmetic of elliptic curves. Since H. Poincare defined the Rang of elliptic curves and proposed the problem, to what number should be attained by Rang, it have been a important theme of algebraic geometry to get the upper bound of the Rang. L.J. Mordell proved the finiteness of that number but the boundedness has not been showed tillnow. By this reason the research is carried on to seak examples of elliptic curves with possiblly large rank. Tate & Shafarevich'sresult on the case of rational function field suggests the unboundedness of the rank of elliptic curves in general, but I am sorry not to have any answer to this problem now. For the reseach in the future it seams to be very important to investigate the historical development and clearify the results of research at present.
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