2013 Fiscal Year Final Research Report
Higher Chow groups and higher dimensional class field theory
| Project/Area Number |
22684001
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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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 |
TAKAO Yamazaki 東北大学, 理学(系)研究科(研究院), 教授 (00312794)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 数論幾何学 / 高次元類体論 / 高次 Chow 群 / ブラウアー群 / K-群 / モチビックホモロジー / モチーフ |
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| Research Abstract |
Higher Chow groups of varieties are important objects in arithmetic geometry in general. When the base field is of arithmetic nature, higher Chow groups are known to be related with arithmetic objects such as the fundamental group and Brauer group. Over a local field, such relation has been studied for smooth projective varieties. We extended it to non-projective varieties. Besides, in a joint work with Bruno Kahn, we described the tensor product in the triangulated category of motives in terms of Somekawa K-groups, which provides us with a new method to compute the higher Chow groups of a product of varieties.
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