2001 Fiscal Year Final Research Report Summary
On the study of cohomology of Chevalley groups using the etale cohomology thoery
| Project/Area Number |
12640025
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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 | OKAYAMA UNIVERSITY |
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Principal Investigator |
MIMURA Mamoru Okayama University, Facility of Science, Professor, 理学部, 教授 (70026772)
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| Co-Investigator(Kenkyū-buntansha) |
KURIBAYASHI Katsuhiko Okayama University, Facility of Science, assistant Professor, 理学部, 助教授 (40249751)
YOSHIOKA Iwao Okayama University, Facility of Science, assistant Professor, 理学部, 助教授 (70033199)
SHIMAKAWA Kazuhisa Okayama University, Facility of Science, Professor, 理学部, 教授 (70109081)
NISHIMOTO Tetsu Kinki Wellfare University, assistant, 社会福祉学部, 助手 (80330520)
TEZUKA Michishige University of Ryukyus, Facility of Science, Professor, 理学部, 教授 (20197784)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Chevalley group / cohomology of group / spectral sequence |
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| Research Abstract |
The research project is to determine the cohomology of (the classifying space of) finite Chevalley groups, which consists of the following.
(1) to construct, using the notion of algebraic geometry, the spectral sequence converging to the cohomology of (the classifying space of) finite Chevalley groups ;
(2) to construct a complex giving the second term of the spectral sequence ;
(3) to show the triviality of the spectral sequence.
As for (1), we have succeeded in constructing the spectral sequence converging to the simplicial scheme which is the model of the Borel construction, by using the Deligne spectral sequence which is the algebraic version of the Eilenberg-Moore spectral sequence.
Furthermore we use the Hochschild spectral sequence to show the triviality of the above spectral sequence, and thus we have succeeded in obtaining the spectral sequence mentioned in the above.
As for (2), we have constructed concretely complexes giving the second term of the spectral sequence for all the cases of spinor type and of exceptional type.
Finally, as for (3), we have some ideas to show the triviality of the spectral sequence by introducing some cohomology operations into the spectral sequence, which may need some more studies in the future.
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