Study of polynomial rings using higher derivations
| Project/Area Number |
24740022
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
Kuroda Shigeru 首都大学東京, 理工学研究科, 教授 (70453032)
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 多項式環 / 正標数 / 高階導分 / 局所冪零導分 / 多項式自己同型 / 線形化問題 / 安定座標 / アフィン代数幾何学 / 不変式 / 局所有限反復高階導分 / 消去問題 / 多項式環論 / 標数位数自己同型 / モジュラー不変式論 |
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| Outline of Final Research Achievements |
Many of the basic problems in polynomial ring are still unsolved, and are studied systematically as difficult problems in Commutative Ring Theory or Algebraic Geometry. In the study of polynomial rings, techniques based on degrees and derivations are effective, but are often not applicable to positive characteristic cases. In this research, we used "higher derivations" effectively in addition to the previous techniques. We studied wide range of problems in polynomial rings including positive or arbitrary characteristic cases, and obtained various new results.
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Report
(5 results)
Research Products
(42 results)
