2009 Fiscal Year Final Research Report
Higher Chow groups of varieties over local fields
| Project/Area Number |
19740002
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Tohoku University |
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Principal Investigator |
YAMAZAKI Takao Tohoku University, 大学院・理学研究科, 准教授 (00312794)
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| Project Period (FY) |
2007 – 2009
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| Keywords | 数論幾何学 / 高次元類体論 / 高次Chow群 / Brauer群 / K-群 |
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| Research Abstract |
Higher Chow groups of varieties is a wide generalization of the ideal class group in the algebraic number theory, and are regarded as a fundamental research theme. When varieties are defined over a local field, it naturally appears in arithmetic context, such as the higher dimensional class field theory and Brauer-Manin pairing. We developed the class field theory for a product of curves, and the Brauer-Manin pairing for open varieties (which was previously considered only for complete varieties).
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