| 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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| 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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