Application of theory of elliptic curves to algebraic topology
Project/Area Number  02640071 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
代数学・幾何学

Research Institution  University of Osaka Prefecture 
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)

CoInvestigator(Kenkyūbuntansha) 
谷口 和夫 大阪府立大学, 総合科学部, 講師 (80079037)
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)
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)
TAKAHASHI Tetsuya University of Osaka Prefecture College of integrated arts and sciences Assistant, 総合科学部, 講師 (20212011)

Project Fiscal Year 
1990 – 1991

Project Status 
Completed(Fiscal Year 1991)

Budget Amount *help 
¥1,100,000 (Direct Cost : ¥1,100,000)
Fiscal Year 1991 : ¥200,000 (Direct Cost : ¥200,000)
Fiscal Year 1990 : ¥900,000 (Direct Cost : ¥900,000)

Keywords  Elliptic curve / Elliptic cohomology / Homotopy / Groupoid scheme / Formal group / Lie group / Automorphic representation / 楕円曲線 / 楕円的コホモロジ / ホモトピ / 亜群スキム / 形式群 / リ群 / 保型表現 / ホモロジ / 形成群 
Research Abstract 
In the research, we developed the theory of groupoid schemes and Hopfalgebroid 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 WeilTaniyama conjecture, We obtained a character formula of cuspidal unramified series of simple algebras over nonaxchimedean 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.

Report
(4results)
Research Output
(20results)