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 |
Research Field |
Algebra
|
Research Institution | Kyoto University |
Principal Investigator |
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Project Period (FY) |
2014-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
|
Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
|
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 / トロピカル化写像 / 忠実トロピカル化 / ベルコビッチ解析空間 / トロピカル化 / 骨格 / 極限トロピカル化 / 線形系 / 国際研究者交流(フランス、イタリア) |
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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Report
(5 results)
Research Products
(25 results)