2013 Fiscal Year Final Research Report
Congruence relations between p-adic crystalline representations
| Project/Area Number |
23740025
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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 | Kyushu University |
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Principal Investigator |
HATTORI Shin 九州大学, 数理(科)学研究科(研究院), 助教 (10451436)
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| Project Period (FY) |
2011 – 2013
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| Keywords | Galois表現 / 合同 / 分岐 |
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| Research Abstract |
Let p be a rational prime number. In this project, I studied various congruence relations between p-adic Galois representations of complete discrete valuation fields. P-adic Galois representations are important objects for number theory. The aim of this project is to develop methods to reduce study of Galois representations to easier cases by using congruence relations. As the most important achievement in this project, I proved an isomorphism between absolute Galois groups of complete discrete valuation fields of mixed and equal characteristics modulo ramification subgroups. This result enables us to reduce study of Galois representations for complete discrete valuation fields of mixed (resp. equal) characteristic to that for equal (resp. mixed) characteristic.
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