2023 Fiscal Year Final Research Report
the rationality problem for fields of invariants
| Project/Area Number |
20K03511
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | 数論 / 代数幾何 / 計算数学 / 有理性問題 / Hasseノルム原理 / ノルム1トーラス |
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| Outline of Final Research Achievements |
(1)This is a joint work with Hoshi Akinari at Niigat University and Kanai Kazuki at Kure College. Let k be a number field,K/k be an extension of degree at most 15, we determined a necessary and sufficient condition for the Hasse norm principle for K/k.
(2)This is a joint work with Hoshi Akinari at Niigata University and Sumito Hasegawa. Let K/k be an extension of degree at most 15. We determined a complete answer to the rationality problem up to stable k-equivalence for norm one tori $R_{K/k}^{(1)}(G_m)$ of K/k.
(3)This is a joint work with Hoshi Akinari at Niigata University. We determined a complete answer to the rationality problem up to stable k-equivalence for norm one tori $R_{K/k}^{(1)}(G_m)$ of K/k whose Galois closures L/k are dihedral extensions.
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| Free Research Field |
代数学 特に数論
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| Academic Significance and Societal Importance of the Research Achievements |
K/kのハッセノルム原理は数論でよく知られた問題だが,[K:k]が6以下の場合や素数の場合など特別な場合しか知られていなかった.特に[K:k]=8,12の場合はほとんど知られていなかった.本研究では主にYu. A. Drakokhrust, V. P. Platonovの結果に従って計算機も用いてdegree 15まで網羅的に決定した.
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