1990 Fiscal Year Final Research Report Summary
Topological Study of K-Theory
| Project/Area Number |
01540038
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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 | Kyoto University |
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Principal Investigator |
NISIDA Goro Kyoto Univ, Fac. of Sci., Prof., 理学部, 教授 (00027377)
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| Co-Investigator(Kenkyū-buntansha) |
HARADA Masana Kyoto univ., Fac. of Sci., Instructor, 理学部, 助手 (80181022)
IRIE Kouyemon Kyoto Univ., Fac. of Sci., Instructor, 理学部, 助手 (40151691)
KONO Akira Kyoto Univ., Fac. of Sci., Lecturer, 理学部, 講師 (00093237)
MARUYAMA Masaki Kyoto Univ., Fac. of Sci., Prof., 理学部, 教授 (50025459)
TODA Hiroshi Kyoto Univ., Fac. of Sci., Prof., 理学部, 教授 (60025236)
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| Project Period (FY) |
1989 – 1990
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| Keywords | Elliptic Cohomology / Modular Forms / K-Theory / Homotopy group / Hecke Operator / Steenrod Operation / Loop Group / Lie group |
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| Research Abstract |
Nishida has studied the elliptic cohomology theory and the theory of modular forms from the homotopical view point following the study of the previous year. A relation between the ring of modular forms and the real cohomology of a certain space was already known, but this year we studied this relation for the mod p case. As one result, we have shown that the trace formula for the Hecke operators after reducing mod p, can be described by the mod p cohomology of the space mentioned above using the Steenrod operations.
On the other hand the theory of p-adic modular forms defined by Serre is closely related to the K-theory. We have defined a p-adic completion of the above space using the mod p K-theory and computed the stable homotopy group. This p-adic homotopy group is quite similar to the group of p-adic modular forms and we hope that these are actually isomorphic.
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