2017 Fiscal Year Final Research Report
Nonarchimedean geometry and its application to arithmetic of algebraic varieties
| Project/Area Number |
26800012
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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 | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | 幾何的ボゴモロフ予想 / ボゴモロフ予想 / 高さ / 非アルキメデス的幾何 / ベルコビッチ空間 / トロピカル幾何 |
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| Outline of Final Research Achievements |
There are two main research results. One concerns the geometric Bogomolov conjecture, and the other concerns tropicalizations of Berkovich spaces.
The geometric Bogomolov conjecture is a conjecture about the distribution of small arithmetic complexity among common zeros of several polynomials and was proposed by Bogomolov around 1980. As research results, I proved important result on this conjecture.
Tropicalizations of Berkovich spaces approximately describe the set of common zeros of several power series in terms of linear inequalities. I established, with Shu Kawaguchi, a nontrivial sufficient condition for such descriptions to sufficiently well approximate the original common zeros.
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| Free Research Field |
代数幾何
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