| Project/Area Number |
09640011
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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 | University of Tokyo |
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Principal Investigator |
SAITO Takeshi Univ.of Tokyo, Ass.Professor, 大学院・数理科学研究科, 助教授 (70201506)
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| Co-Investigator(Kenkyū-buntansha) |
KURIHARA Masato Tokyo Metro.Univ., Ass.Professor, 理学部, 助教授 (40211221)
SAITO Shuji Tokyo Inst.of Tech.Professor, 理学部, 教授 (50153804)
ODA Takayuki Univ.of Tokyo, Professor, 大学院・数理科学研究科, 教授 (10109415)
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| Project Period (FY) |
1997 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 1998: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 1997: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | Hilbert modular form / Langlands correspondence / Galois representations / Shimura curves / p-adic Hodge theory / etale cohomology / Stiefel-Whitney class / conductor / Hilbert 保型形式 / Langlands 対応 / Galois 表現 / エチールコホモロジー / P進Hodge理論 |
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| Research Abstract |
The main result is obtained in the research on the l-adic representation associated a Hilbert modular form. It is a 2-dimensional l-adic representation of the absolute Galois group G_F of a totally real field F.For a finite place upsilon * l, it is shown by Carayol that the representation of the Weil-Deligne group defined by its restriction to the decomposition group at upsilon corresponds to the upsilon-component of the automorphic representation of GL_2 (A_F) determined by f. Using recent results in p-adic Hodge theory, I formulated a similar statement and proved it. The second year of the project was spent to write a paper and paper is nearly completed.
As a byproduct of the proof, I proved the monodromy-weight conjecture for Galois representation associated to modular forms. It seems to have been overlooked even for the case F=Q.The paper is already to appear in a Proceedings.
I also obtained some other results. For an algebraic variety X over a field K, the second Stiefel-Whitney class of its l-adic etale cohomology is defined in the second Galois cohomology H^2 (K, Z/2Z). I formulated a conjecture between the class with the Hasse-Witt class of de Rham cohomology and proved it in several cases.
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