| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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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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