Arithmetic geometry of covers of algebraic curves--Galois representations, Hurwitz spaces, and positive characteristic
| Project/Area Number |
18540027
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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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 |
TAMAGAWA Akio Kyoto University, 数理解析研究所, 教授 (00243105)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,220,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥720,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
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| Keywords | 代数曲線 / 被覆 / 基本群 / ガロア表現 / フルビッツ空間 / 正標数 / 国際研究者交流 / 米国:仏国:英国 / 米国:仏国:英国:韓国 / 米国:仏国:英国:ハンガリー |
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| Research Abstract |
The original main aim of the present research project was to develop my three joint researches ("Galois representations", "Hurwitz spaces", "positive characteristic") on arithmetic geometry of covers of algebraic curves with three respective foreign collaborators -- C. Rasmussen (USA), A. Cadoret (France) and M. Saidi (UK). Actually, through their visits to Japan and my visits to France and UK, we have developed our joint researches and obtained several nice results concerning a finiteness conjecture for abelian varieties related to Ihara's problem ; the modular tower conjecture on rational points of Hurwitz spaces ; a uniform boundedness problem for Galoir representations ; positive-characteristic and p-adic anabelian geometry and so on.
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Report
(6 results)
Research Products
(34 results)
