| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
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| Outline of Final Research Achievements |
Heights are considered to measure arithmetic "bigness" or "complexity" of points and subvarieties of algebraic varieties defined over number fields. For a dominant rational self-map of an algebraic variety, there is a basic notion called the "dynamical degree" of the map, which measures the degree growth rate under the iteration of the self-map. With joint works with J. H. Silverman, we have studied relationship between the dynamical degree and the "arithmetic degree" of a rational point, which measures the height growth rate of a rational point under the iteration of the self-map. For abelian varieties, we have studied this relationship in more detail.
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