Study on arithmetic geometry by arithmetic cohomology
| Project/Area Number |
20540025
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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 | Tokyo Denki University |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 数論幾何 / p進Steenbrink-Mokrane複体 / Clemens-Schmid系列 / 剛性コホモロジー / p進モノドロミー重み予想 / p進対数強Lefschetz予想 / 分裂単体的半安定多様体 / 層係数p進Steenbrink複体 / 層係数p進Steenbrink系列 / 擬モノドロミー作用素 / 相対Clemens-Schmid系列 / 単数根F-クリスタル / Steenbrink-Mokrane複体 / コホモロジー / 収束トポス / p進純粋性 / 半安定型多様体 / p進重み複体 / p進重み系列 / 基礎対数スキームの系列 / p進Steenbrink重み複体 / p進Steenbrkink重み系列 / E2退化 / p進Steenbrkink-Mokrane重み複体 / 無限小コホモロジー / 兵藤加藤の同型射 / 多様体の分解 / 擬大域チャート / 対数的収束トポス / 重み付き消滅サイクル / 擬態域チャート / 仮想ベッチ数 / 単体的安定多様体 |
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| Research Abstract |
In arithmetic geometry(=the conjunction of arithmetic andgeometry), there is a theory of p-adic cohomology. For this theory, we have constructed afundamental theory of logarithmic convergent topoi and proved various properties oflogarithmic weight filtration. We have also constructed the p-adic weight spectralsequences of proper varieties with any singularities over the fraction field of a completediscrete valuation ring of mixed characteristics and proved the fundamental properties ofit.
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Report
(7 results)
Research Products
(20 results)
