Canonical heights and algebraic/arithmetic dynamics
Project/Area Number |
24740015
|
Research Category |
Grant-in-Aid for Young Scientists (B)
|
Allocation Type | Multi-year Fund |
Research Field |
Algebra
|
Research Institution | Kyoto University |
Principal Investigator |
KAWAGUCHI Shu 京都大学, 理学(系)研究科(研究院), 准教授 (20324600)
|
Project Period (FY) |
2012-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
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)
|
Keywords | 標準的高さ / Arakelov 幾何 / Arakelov幾何 / アラケロフ幾何 / 解析的トーション |
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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Report
(4 results)
Research Products
(20 results)