| Project/Area Number |
25887009
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TSUSHIMA TAKAHIRO 東京大学, 数理(科)学研究科(研究院), 助教 (70583912)
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| Project Period (FY) |
2013-08-30 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | ガロワ表現 / Lubin-Tate perfectoid空間 / 局所ラングランズ対応 / 局所ジャッケ・ラングランズ対応 / タイプ理論 / 局所ラングランズ対応の幾何実現 |
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| Outline of Final Research Achievements |
We have studied Galois representations in a view point of Langlands program. More concretely, we have studied the local Langlands correspondence and the local Jacquet-Langlands correspondence geometrically through geometry of Lubin-Tate perfectoid space. An epipelagic representation means an easiest cuspidal representation of ramified type of a general linear group over a non-archimedean local field. For such representations, we have constructed a family of affinoids and its formal models, and studied the middle cohomology of the reductions of the models in a representation theoretic view point. As a result, we have constructed two correspondences between representations. We have proved that one of them corresponds to the local Jacquet-Langlands correspondence for epipelagic representations. As a by-product, we have shown the B-S-S conjecture for epipelagic representations. This conjecture asserts the compatibility of types under the local Jacquet-Langlands correspondence.
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