| Project/Area Number |
18340002
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | The University of Tokyo |
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Principal Investigator |
SAITO Takeshi The University of Tokyo, 大学院・数理科学研究科, 教授 (70201506)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Kazuya 京都大学, 大学院・理学研究科, 教授 (90111450)
SAITO Shuji 東京大学, 大学院・数理科学研究科, 教授 (50153804)
TERASOMA Tomohide 東京大学, 大学院・数理科学研究科, 教授 (50192654)
TSUJI Takeshi 東京大学, 大学院・数理科学研究科, 准教授 (40252530)
SHIHO Atsushi 東京大学, 大学院・数理科学研究科, 准教授 (30292204)
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| Project Period (FY) |
2006 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥17,120,000 (Direct Cost: ¥14,000,000、Indirect Cost: ¥3,120,000)
Fiscal Year 2009: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2008: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2007: ¥7,410,000 (Direct Cost: ¥5,700,000、Indirect Cost: ¥1,710,000)
Fiscal Year 2006: ¥3,600,000 (Direct Cost: ¥3,600,000)
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| Keywords | 数論幾何学 / 代数学 / 整数論 / 導手 / 局所体 / l進層 / 分岐 / Kummer被覆 / Swan類 / 代数幾何学 / 1進コホモロジー / e進層 / 切除公式 / ガロワ表現 / 1進フーリエ変換 / ε因子 / エタール・コホモロジー / 1-進層 / 特性サイクル・特性類 / Galois表現 / 導手公式 / 不確定特異点 |
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| Research Abstract |
I studied the structure of graded quotients of the filtration by ramification groups of the absolute Galois group of a local field. Using this, I defined the characteristic variety of an l-adic sheaf under some condition and computed the characteristic class as the intersection product with the 0-section.
For an arbitrary constructible sheaf on a variety over a local field, I defined the Swan class and proved a formula of Riemann-Roch type formula in a relative version.
I computed explicitly as an induced representation the local Fourier transform of an l-adic representation of the absolute Galois group of a local field of positive characteristic, under a certain assumption.
For the p-adic Galois representation associated to a Hilbert modular form, I published a paper establishing the compatibility with the local Langlands correspondence at a prime dividing p in the sense of p-adic Hodge theory
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