2012 Fiscal Year Final Research Report
p-adic cohomology and Langlands' correspondence
| Project/Area Number |
23840006
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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 |
ABE Tomoyuki 東京大学, 数物連携宇宙研究機構, 特任助教 (70609289)
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| Project Period (FY) |
2011 – 2012
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| Keywords | 進コホモロジー / D 加群 / ラングランズ対応 |
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| Research Abstract |
In this work, I tried to construct a foundational theory of p-adic cohomology. First, I proved the Cebotarev density type theorem, which states that we can retrieve p-adic differential equation when we look at the Frobenius action, and established the theory of weights in p-adic cohomology theorem as well as the purity for the intersection cohomology. These results are expected to be applied to the “petits camarades conjecture” by Deligne claiming that the p-adic and l-adic cohomology theories have essentially the same information.
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