2001 Fiscal Year Final Research Report Summary
Arithmetic Study of Interactions of Galois groups and anabelian geometry
| Project/Area Number |
12640033
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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 | Tokyo Metropolitan University |
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Principal Investigator |
NAKAMURA Hiroyuki Graduate School of Science, Tokyo Metropolitan University Associate Professor, 理学(系)研究科(研究院), 助教授 (60217883)
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| Co-Investigator(Kenkyū-buntansha) |
KAWASHIMA Takeshi Graduate School of Science, Tokyo Metropolitan University Assistant Professor, 理学(系)研究科(研究院), 助手 (40301410)
TAKEDA Yuichiro Graduate School of Science, Tokyo Metropolitan University Assistant Professor, 理学(系)研究科(研究院), 助手 (30264584)
KURATA Toshihiko Graduate School of Science, Tokyo Metropolitan University Assistant Professor, 理学(系)研究科(研究院), 助手 (40311899)
ITO Yukari Graduate School of Science, Tokyo Metropolitan University Assistant Professor, 理学(系)研究科(研究院), 助手 (70285089)
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| Project Period (FY) |
2000 – 2001
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| Keywords | Galois representation / Galois group / Exterior Galois representation / Anabelian Geometry / Mapping Class Group / Teichmuller modular group / Arithmetic Fundamental Group / Grothendieck-Teichmuller group |
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| Research Abstract |
1. I wrote up results on the standard tangential base points constructed in the moduli spaces of algebraic curves. These tangential base points are constructed to give standard Galois representations in the profinite Teichmueller modular groups. This is compatible with topological description in terms of Dehn twists and the parameters of the Grothendeick Teichmueller group previously obtained in my collaboration with L.Schneps, P.Lochak. The resultant paper was submitted to Proc. Symp. Pure Math. And has been accepted in publication there.
2. I also developed studies on exterior monodromy representations of arithmetic fundamental groups arising from continuous families of elliptic curves. In particular, I proved an explicit formula describing a certain power series representation by Kummer properties of roots of special theta values which reflects the meta-abelain quotient of the above monodromy representation. This is a profinite generalization of the 1-adic formula of my previous result published in 1995 paper.In early September, I made a tplk presenting these results in the Euresco conference near Sapri, Italy. I also found a minute relation between the above power series representation and periods of Eisenstein series. I talked on this result at a workshop at RIMS, Kyoto University at the end of January, 2002.
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Research Products
(8 results)
