2009 Fiscal Year Final Research Report
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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| 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 |
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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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