| Project/Area Number |
24540016
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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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) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 遠アーベル幾何学 / 組み合わせ論的遠アーベル幾何学 / 多重双曲的曲線 / Hodge-Tate性 / 穏やかな点 / 合同部分群問題 / p進Teichmuller理論 / 単遠アーベル幾何学 / Hodge-Tate保存性 / 組み合わせ論的セクション予想 / サイクルの標準持ち上げ / 双曲的代数曲線 / 写像類群 / 三点基 / 組み合わせ論的カスプ化 / テンパード基本群 / グロタンディーク予想 / ホッジ・テイト保存性 |
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| Outline of Final Research Achievements |
(1) I obtained Grothendieck conjecture-type results for hyperbolic polycurves over sub-p-adic fields, p-adic local fields, and hyperbolic curves over Kummer-faithful fields. (2) By a joint work with Shinichi Mochizuki, we developed combinatorial anabelian geometry. (3) I studied the kernels and images of the outer Galois actions associated to hyperbolic curves and proved the finiteness of the moderate rational points of a hyperbolic curve over a number field. (4) As a joint work with Yu Iijima, we studied a pro-p version of the congruence subgroup problem. (5) I studied nilpotent admissible indigenous bundles, as well as nilpotent ordinary indigenous bundles, which is a central object in p-adic Teichmuller theory, in characteristic three. (6) I developed mono-anabelian geometry for number fields.
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