Arithmetic of hyperbolic algebraic curves related to arithmetic fundamental groups
| Project/Area Number |
15K04780
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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, 准教授 (50456761)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 双曲的代数曲線 / 数論的基本群 / 遠アーベル幾何学 / p進Teichmuller理論 / 休眠乍 / 等分点 / 巾零通常固有束 / 射影構造 / 単遠アーベル的復元アルゴリズム / 超特異因子 / Frobenius的射影構造 / 圏論的特徴付け / 副p絶対遠アーベル幾何学 / 遠アーベル予想 / 組み合わせ論的遠アーベル幾何学 / GT群 / 単遠アーベル幾何学 / Grothendieck予想 / 双曲的多重曲線 / 当分点 / 有限平坦可換群スキーム / 対数スキーム / 狭義射 |
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| Outline of Final Research Achievements |
(1) I proved uniqueness of dormant opers of rank p-1 on a projective hyperbolic curves in characteristic p. (2) I studied torsion points on algebraic curves that have good reduction over absolutely unramified bases. (3) I obtained a certain categorical representation of log schemes. (4) I obtained categorical characterizations of isomorphism classes of local fields. (5) I established a pro-p criterion for good reduction of ordinary curves. (6) I solved the anabelian conjecture for moduli spaces of elliptic curves equipped with additional data. (7) I developed combinatorial anabelian geometry. (8) I gave a characterization of supersingular divisors of nilpotent ordinary indigenous bundles. (9) I established a certain positive characteristic analogue of theory of projective structures on Riemann surfaces. (10) I studied the anabelian geometry of local fields.
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Report
(4 results)
Research Products
(34 results)
