2011 Fiscal Year Final Research Report
An research of regulator maps on arithmetic varieties
| Project/Area Number |
21540019
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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 | Kyushu University |
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Principal Investigator |
YUICHIRO Takeda 九州大学, 大学院・数理学研究院, 准教授 (30264584)
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| Project Period (FY) |
2009 – 2011
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| Keywords | レギュレーター写像 / 代数サイクル / 代数的K理論 |
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| Research Abstract |
The regulator map is one of the most interesting object of research in arithmetic geometry. In this research we have shown that the regulator map is described as integrals over algebraic cycles. Moreover, we have established a higher extension of the theory of arithmetic Chern character of a hermitian vector bundle on an arithmetic variety. In other words, we have constructed a homomorphism from higher arithmetic K-group to higher arithmetic Chow group. This can be seen as an analogue of regulator map in Arakelov geometry.
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