Arithmetic D-modules and Langlands correspondence
| Project/Area Number |
25800004
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Abe Tomoyuki 東京大学, カブリ数物連携宇宙研究機構, 准教授 (70609289)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | p進コホモロジー / 関数体のラングランズ対応 / 数論的D加群 / ラングランズ対応 / アイソクリスタル |
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| Outline of Final Research Achievements |
We constructed a Langlands type correspondence for p-adic coefficient theory for function fields, and as a result, I resolved Deligne's crystalline companion conjecture for curves. This was nothing but the goal of this research, and we may say that I attained it. This correspondence enables us an p-adic interpretation of cohomology theories over finite fields, and opened a new door of the theory.
The main result states that there exists a correspondence between overconvergent F-isocrystals and cuspidal automorphic representations. However, in the proof, the category of overconvergent isocrystals is too small, and we need to deal with a much wider class called the arithmetic D-modules. In the work, by completing the program of Berthelot on the construction of such theory, we were able to obtain the desired result.
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Report
(5 results)
Research Products
(19 results)
