2012 Fiscal Year Final Research Report
On a finiteness of certain abelian varieties anda classification of certain Galois representations
| Project/Area Number |
23840028
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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 | Kyoto University (2012)
Kyushu University (2011) |
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Principal Investigator |
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| Project Period (FY) |
2011 – 2012
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| Keywords | アーベル多様体 / ガロア表現 / Liu 加群 |
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| Research Abstract |
I studied a special case of a conjecture of Rasmussen-Tamagawa, which is related with a finiteness of certain abelian varieties. More precisely, I gave a criterion for two Galois representations of an algebraic number field to be isomorphic when restricted to a decomposition group, in terms of a global representations mod l. This is applied to prove a generalization of the conjecture. On the other hand, I studied a linear algebraic properties of Liu modules, which classifies certain torsion Galois representations. Furthermore, I studied torsion crystalline representation s via Liu modules and obtained a full faithfulness theorem for them. It is a torsion analogue of a Breuil conjecture proved by Kisin in 2006.
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