2012 Fiscal Year Final Research Report
Study on p-adic cohomology, homotopy and overconvergent isocrystals
| Project/Area Number |
21740003
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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 | The University of Tokyo |
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Principal Investigator |
SHIHO Atsushi 東京大学, 大学院・数理科学研究科, 准教授 (30292204)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 過収束アイソクリスタル / 対数的収束アイソクリスタル / 対数的構造 / p進微分方程式 / p進表現 / 可積分接続 / p進非リュービル数 |
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| Research Abstract |
I proved the following results on overconvergent isocrystal, which is a certain p-adic differential equation. First, I proved the theorem of logarithmic extension for overconvergent isocrystals. Next I proved the theorem of cut-by-curves criterion for the log extendability of overconvergent isocrystals and the overconvergence of modules with integrable connections. Moreover, I proved a kind of purity theorem for overconvergent F-isocrystals. I defined the category of certain parabolic unit-root log convergent F-isocrystals and proved that it is equivalent to the category of tamely ramified p-adic representations of fundamental groups. Also, I proved a certain generalization of a result of Ogus-Vologodsky on the category of modules with integrable connection and the category of Higgs modules.
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