An research of regulator maps on arithmetic varieties
Project/Area Number |
21540019
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Kyushu University |
Principal Investigator |
YUICHIRO Takeda 九州大学, 大学院・数理学研究院, 准教授 (30264584)
|
Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
|
Keywords | レギュレーター写像 / 代数サイクル / 代数的K理論 / アラケロフ幾何学 / チャウ群 / 多重対数関数 |
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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Report
(4 results)
Research Products
(6 results)