Study of the moduli of Galois representations of number fields and function fields
| Project/Area Number |
25400016
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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 | Kyushu University |
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Principal Investigator |
Taguchi Yuichiro 九州大学, 数理(科)学研究科(研究院), 准教授 (90231399)
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| Co-Investigator(Kenkyū-buntansha) |
HATTORI Shin 九州大学, 大学院数理学研究院, 助教 (10451436)
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| Co-Investigator(Renkei-kenkyūsha) |
KURIHARA Masato 慶應大学, 理工学部, 教授 (40211221)
SAITO Takeshi 東京大学, 大学院数理科学研究科, 教授 (70201506)
TAMAGAWA Akio 京都大学, 数理解析研究所, 教授 (00243105)
YASUDA Seidai 大阪大学, 大学院理学研究科, 准教授 (90346065)
HIRANOUCHI Toshiro 広島大学, 大学院理学研究科, 助教 (30532551)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
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| Keywords | ガロア表現 / モジュライ / 有限性 / 代数体 / 函数体 / ヘッケ体 / 数論 / 保型表現 |
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| Outline of Final Research Achievements |
We have constructed a moduli scheme of Galois representations and studied its properties, and obtained some basic results. We have also obtained several related results, such as: (1) a vanishing theorem of the Galois-fixed subspace of a Galois representation of a rather general type of complete discrete valuation field (a generalization of a theorem of Imai) and its application to Iwasawa theory, (2) a result on the congruence of Galois representations and its application to non-existence theorems a la Rasmussen-Tamagawa, (3) proof of the fact that the Hecke field of a geometric Galois represntation is often (say, with density 1 primes, in certain cases) generated by the trace of the Frobenius for a single finite prime, (4) an upper bound of the number of the connected components of the Zariski closure of the image of a Galois representation.
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Report
(4 results)
Research Products
(14 results)
