2018 Fiscal Year Final Research Report
Cultivation of computational approaches in constructive Galois theory and arithmetic fundamental groups
| Project/Area Number |
16K13745
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka University |
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Principal Investigator |
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| Research Collaborator |
OGAWA Hiroyuki 大阪大学, 大学院理学研究科, 助教
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | 実験数学 |
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| Outline of Final Research Achievements |
We made computational approaches to various arithmetic-geometric objects related to finite ordered points on elliptic curves and/or Jacobian varieties, including periodic continued fractional expansions about specific polynomial Pell equations, algebraic deformation of Poncelet polygons, Diophantine equations related to arithmetic of elliptic curves. Using intersections of cevians of plane triangles, we obtained basic properties of certain triangle operations with two complex variables together with visual outputs of iteration of area preserving operators.
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| Free Research Field |
整数論
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| Academic Significance and Societal Importance of the Research Achievements |
この研究では構成的ガロア理論や数論的基本群（遠アーベル幾何）をめぐる様々な数論現象の研究のうち，計算代数的な手法で発見的に対象を構成できる題材の開拓を目指す．代数多様体の基本群を形作る対称性や代数的被覆写像の系列に関連して見えてくる構造のうち，計算代数的な観点から表現できるものを実験的に検証し，具体的なヴィジュアル出力を含め実例計算を示すことにより，周辺分野の専門家や若手研究者を含む幅広い研究者層の理解と興味を促進する．
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