2012 Fiscal Year Final Research Report
Research on heights on algebraic varietiesfrom the viewpoint of Arakelov geometry and its application
| Project/Area Number |
21740012
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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 | Kyoto University |
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Principal Investigator |
YAMAKI Kazuhiko 京都大学, 高等教育研究開発推進機構, 准教授 (80402973)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 代数幾何 |
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| Research Abstract |
On an algebraic variety, which is a geometric object defined by algebraic equations, we sometimes have “height functions”. These height functions measure arithmetic complexity of varieties. Using them, we can study relationships between the distribution of small algebraic points and the geometric property of the variety. In this research, we investigated the heights of some important subjects in algebraic geometry. Furthermore, we applied the results on heights to interesting arithmetic problems, obtaining significant results.
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