Research on algebraic cycles on arithmetic schemes
| Project/Area Number |
20740008
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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 | Chuo University (2010)
Nagoya University (2008-2009) |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2009: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 数論幾何学 / 代数学 / 整数論 / 数論的代数幾何 / 代数的サイクル / コホモロジー |
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| Research Abstract |
We study arithmetic properties, including finiteness, of the Chow group of 1-cycles on arithmetic schemes, especially regular semistable families on p-adic integer rings. The main tool in in this approach is the cycle class map to the etale cohomology. We derive properties of cycles by showing the injectivity and surjectivity of this cycle class map. In fact, we obtained a stong l-adic property of the 1-cycles in some quite general situation, and were able to compute the Chow group of 0-cycles on some special rational surface over a p-adic field.
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Report
(5 results)
Research Products
(34 results)
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[Presentation] ガロアコホモロジー2009
Author(s)
佐藤周友
Organizer
第17回整数論サマースクール
Place of Presentation
アピカルイン京都(京都市左京区)
Year and Date
2009-08-18
Related Report
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