2010 Fiscal Year Final Research Report
Application of p-adic differential equations to number theory
| Project/Area Number |
19540010
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Chiba University |
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Principal Investigator |
MATSUDA Shigeki Chiba University, 大学院・理学研究科, 准教授 (90272301)
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| Project Period (FY) |
2007 – 2010
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| Keywords | 数論 |
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| Research Abstract |
Let k be a filed of Laurent series with several variables over an algebraically closed field of positive characteristic and let E be a complete discrete valuation ring of equal characteristic with residue field k. We defined a filtration for a differential module over the Robba ring with residue filed E with respect to the irregularity, which generalized classical filtration defined by Christol and Mebkhout. Then we showed that the filtration coincides with the filtration that comes from the Abbes-Saito filtration on the solution space regarded as Galois module when the differential module can be trivialized by the finite separable extension of the residue field E.
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