2011 Fiscal Year Final Research Report
Arithmetic and Combinatorial Study of Anabelian Geometry
| Project/Area Number |
22740012
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyoto University |
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Principal Investigator |
HOSHI Yuichiro 京都大学, 数理解析研究所, 講師 (50456761)
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| Project Period (FY) |
2010 – 2011
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| Keywords | 双曲的曲線 / 数論的基本群 / 配置空間群 / 組み合わせ論的遠アーベル幾何学 / 副有限デーン捻り / モノドロミー充満 / セクション予想 / 双有理セクション予想 |
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| Research Abstract |
By a joint work with Shinichi Mochizuki, I developed the fundamental theory of the combinatorial anabelian geometry. As an application of this theory, I and Shinichi Mochizuki proved a geometric version of Grothendieck's anabelian conjecture for the universal curve over the moduli stack of pointed curves. In the study of the monodromic fullness of hyperbolic curves, I gave a counter-example of the problem of the l-independency of quasi-monodromic fullness. In the study of the birational section conjecture for curves over number field, I obtained a necessary and sufficient condition for a birational Galois section of a curve over a small number field to be geometric.
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