2009 Fiscal Year Final Research Report
Research of arithmetic fundamental groups of hyperbolic curves
| Project/Area Number |
20740010
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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 Kyoto University, 数理解析研究所, 助教 (50456761)
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| Project Period (FY) |
2008 – 2009
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| Keywords | 遠アーベル幾何 / 数論的基本群 / 双曲的曲線 / 配置空間 / 外Galois表現 / 組み合わせ論的カスプ化 / モノドロミー充満 / Galois切断 |
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| Research Abstract |
By a joint work with Shinichi Mochizuki, we proved the injectivity portion of the combinatorial cuspidalization; moreover, as an arithmetic application of this injectivity, we obtained the faithfulness of the outer Galois representations associated to hyperbolic curves over number or p-adic local fields. Next, I introduced the notion of monodromic fullness for hyperbolic curves and proved an anabelian conjecture-type result for certain monodromically full hyperbolic curves of genus zero. Finally, I proved that in general, the pro-p section conjecture for hyperbolic curves over number fields, as well as p-adic local fields, cannot be resolved in the affirmative.
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