Vojta's Conjecture on blowups and in Arithmetic Dynamics
| Project/Area Number |
23740033
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Nihon University |
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Principal Investigator |
YASUFUKU Yu 日本大学, 理工学部, 准教授 (00585044)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | ボエタ予想 / 数論的力学系 / 整数点 / 最大公約数 / モーデル・ラング予想 / 代数学 / ディオファントス幾何 / 国際研究者交流 / アメリカ：カナダ / 整数点と有理点 / 不変多様体 / 高さ関数 / フランス：韓国：アメリカ / アーベル多様体 / ヒルベルト第10問題 / アメリカ：イタリア / 単項式写像 / アメリカ：フランス |
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| Outline of Final Research Achievements |
Diophantine geometry is a study on integral and rational solutions to multivariable polynomials, and Vojta’s conjecture is one of the most important conjectures in this field. During the span of this grant, I have succeeded in proving some cases of Vojta’s conjecture on the blowups of the projective space. I have also analyzed arithmetic properties of orbits, that is, how a point is moved by the iterates of a fixed map. In particular, I have obtained some conditions under which integral points in orbits are sparse, and I have proved that the intersection of orbits and subvarieties do not have any group-like structure as one would expect from the theory of abelian varieties.
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Report
(5 results)
Research Products
(41 results)
