2010 Fiscal Year Final Research Report
Geometric torsion Galois representations and ramification theory
| Project/Area Number |
21740023
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Kyushu University |
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Principal Investigator |
HATTORI Shin Kyushu University, 数理学研究院, 助教 (10451436)
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| Project Period (FY) |
2009 – 2010
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| Keywords | 局所体 / ガロア表現 / 分岐 / 整p進Hodge理論 |
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| Research Abstract |
In this two-year study period, I had investigated a ramification theory of torsion Galois representations of local fields of mixed characteristic (0,p). It is well-known that there exists an inclusion from the category of finite flat group schemes killed by p over the ring of integers of such a local field into a similar category for equal characteristic p. In this research project, I proved that this inclusion preserves ramification of both sides. This enables us to reduce the study of ramification to the much easier case of equal characteristic. As an application of this result, I also proved a new existence theorem of canonical subgroups of Abelian varieties, which is one of the key ingredients of the theory of p-adic Siegel modular forms.
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