2011 Fiscal Year Final Research Report
Arithmetic of modularity lifting and Langlands duality
| Project/Area Number |
21540013
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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 |
YASUDA Seidai 京都大学, 数理解析研究所, 助教 (90346065)
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| Co-Investigator(Kenkyū-buntansha) |
KONDO Satoshi 東京大学, 数物連携宇宙研究機構, 特任助教 (30372577)
TAGUCHI Yuichiro 九州大学, 数理学研究院, 准教授 (90231399)
HIRANOUCHI Toshiro 広島大学, 理学研究科, 助教 (30532551)
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| Co-Investigator(Renkei-kenkyūsha) |
ISHIKAWA Yoshihiro 岡山大学, 自然科学研究科, 助教 (50294400)
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)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 数論幾何学 / L-関数 / ガロア表現 / ε-因子 / 保型表現 / ラングランズ双対性 |
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| Research Abstract |
In a joint work with Go Yamashita, I have determined the reductions modulo p of crystalline representations in many unknown cases, by explicitly constructing Wach modules and by introducing some new methods involving hypergeometric polynomials. I and Satoshi Kondo have succeeded in describing the epsilon factor of irreducible admissible representations as explicit Hecke eigenvalues and in giving several criterion for those representations to have"mirahoric"fixed vectors. I have obtained some other findings in Serre's conjecture and p-adic representations which will be useful in my future study.
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