2012 Fiscal Year Final Research Report
Study of various aspects of Galois representations
| Project/Area Number |
22540024
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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 | Kyushu University |
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Principal Investigator |
TAGUCHI Yuichiro 九州大学, 大学院・数理学研究院, 准教授 (90231399)
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| Co-Investigator(Renkei-kenkyūsha) |
SAITO Takeshi 東京大学, 大学院・数理科学研究科, 教授 (70201506)
HIRANOUCHI Toshiro 広島大学, 大学院・理学研究科, 助教 (30532551)
YASUDA Seidai 大阪大学, 大学院・理学研究科, 准教授 (90346065)
HATTORI Shin 九州大学, 大学院・数理学研究院, 助教 (10451436)
MIEDA Yoichi 京都大学, 白眉センター/大学院・理学研究科, 准教授 (70526962)
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| Project Period (FY) |
2010 – 2012
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| Keywords | 数論 / ガロア表現 |
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| Research Abstract |
We obtained several useful results on Galois representations. In particular, for a geometric Galois representation of a complete discrete valuation fields with imperfect residue field, we proved, under suitable conditions, that its fixed subspace over a ``large'' Kummer extension of the base field is trivial, and applied this to Iwasawa Theory. Moreover, we studied the congruence of Galois representations and obtained some results on the generalization of the Rasmussen-Tamagawa conjecture.
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