1999 Fiscal Year Final Research Report Summary
MORDELL-WEIL LATTICES OF JACOBIAN VARIETIES
| Project/Area Number |
09640073
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | RIKKYO UNIVERSITY |
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Principal Investigator |
SHIODA Tetsuji RIKKYO UNIV. COLLEGE OF SCIENCE, PROFESSOR, 理学部, 教授 (00011627)
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| Co-Investigator(Kenkyū-buntansha) |
AOKI Noboru RIKKYO UNIV. COLLEGE OF SCIENCE, ASSIST. PROFESSOR, 理学部, 助教授 (30183130)
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| Project Period (FY) |
1997 – 1999
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| Keywords | MODELL-WEIL LATTICES / JACOBIAN VARIETIES / SPLITTING FIELDS / UNITS / INTERSECTION THEORY |
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| Research Abstract |
I. Mordell-Weil Lattices of Jacobian Varieties.
Basic Theory and Applications
II. Construction of Jacobian Varieties with high Mordell-Weil Rank. We have established the following :
Theorem For any integer g > 0, there exist infinite family of algebraic curves whose Jacobian varieties have Mordell-Weil rank ≧ 4g + 7.
This result greatly improves Neron's assertion (1954) of existence of curves with rank ≧ 3g + 7.
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