2011 Fiscal Year Final Research Report
canonical heights and related topics
| Project/Area Number |
21740018
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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 | Osaka University |
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Principal Investigator |
KAWAGUCHI Shu 大阪大学, 大学院・理学研究科, 准教授 (20324600)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 標準的高さ / Arakelov幾何 |
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| Research Abstract |
Heights are considered to measure arithmetic" bigness" or" complexity" of points and subvarieties of algebraic varieties defined over number fields. When algebraic varieties have" nice" self-maps, there sometimes exist heights that behave well with respect to the self-maps. Such heights are called canonical heights. We have constructed global and local canonical height functions for affine space regular automorphisms. We have also studied difference of these canonical heights. We have studied degree growth of affine space triangular automorphisms over Q-algebras. For dominant rational maps of algebraic varieties, we have studied arithmetic growth of points with respect to degree growth of the maps.
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