| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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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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