Canonical heights and algebraic/arithmetic dynamics

2014 Fiscal Year Final Research Report

• 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
• Keywords: 標準的高さ / Arakelov 幾何

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.

Free Research Field

代数幾何学