1991 Fiscal Year Final Research Report Summary
Application of theory of elliptic curves to algebraic topology
| Project/Area Number |
02640071
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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 | University of Osaka Prefecture |
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Principal Investigator |
ISHII Noburo University of Osaka Prefecture College of integrated arts and sciences Associate professor, 総合科学部, 助教授 (30079024)
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| Co-Investigator(Kenkyū-buntansha) |
SHINKAI Kenzo University of Osaka Prefecture College of integrated arts and sciences Professor, 総合科学部, 教授 (50079034)
OKANO Hatuo University of Osaka Prefecture College of integrated arts and sciences Professor, 総合科学部, 教授 (40079033)
TAKAHASHI Tetsuya University of Osaka Prefecture College of integrated arts and sciences Assistant, 総合科学部, 講師 (20212011)
YAMAGUCHI Atsushi University of Osaka Prefecture College of integrated arts and sciences Assistant, 総合科学部, 講師 (80182426)
KONNO Yasuko University of Osaka Prefecture College of integrated arts and sciences Associate, 総合科学部, 助教授 (70028231)
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| Project Period (FY) |
1990 – 1991
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| Keywords | Elliptic curve / Elliptic cohomology / Homotopy / Groupoid scheme / Formal group / Lie group / Automorphic representation |
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| Research Abstract |
In the research, we developed the theory of groupoid schemes and Hopf-algebroid related to formal groups of universal elliptic curves and elliptic cohomology. We studied the theory of schemes and sheaves of modules in the category of graded algebras. In application of number theory to algebraic topology, we studied models of universal elliptic curves, automorphic representations over local fields and cohomology groups of locally symmetric spaces. We determined models of elliptic curves of small conductor and that of modular curves deeply connected to elliptic curves through Weil-Taniyama conjecture, We obtained a character formula of cuspidal unramified series of simple algebras over non-axchimedean local fields and a dimension formula of cohomology groups of locally symmetric spaces. Based on those results we studied relation between formal groups of universal elliptic curves and those of automorphic representations. Further we studied automorphic forms using the results newly obtained in the field of differential equations and real analysis.
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