2010 Fiscal Year Final Research Report
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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| Keywords | 数論幾何学 |
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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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