2009 Fiscal Year Final Research Report
Noether's Problem for Cremona Groups over algebraic number fields and its application to Number theory
| Project/Area Number |
19340011
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Waseda University |
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Principal Investigator |
HASHIMOTO Kiichiro Waseda University, 理工学術院, 教授 (90143370)
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| Co-Investigator(Kenkyū-buntansha) |
KOMATSU Keiichi 早稲田大学, 理工学術院, 教授 (80092550)
MURAKAMI Jun 早稲田大学, 理工学術院, 教授 (90157751)
MIYAKE Katsuya (20023632)
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| Co-Investigator(Renkei-kenkyūsha) |
KIDA Masanari 電気通信大学, 教授 (20272057)
TSUNOGAI Hiroshi 上智大学, 理工学部, 准教授 (20267412)
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| Project Period (FY) |
2007 – 2009
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| Keywords | ガロア理論 / ガロアの逆問題 / ネーター問題 / クレモナ変換群 / 有理関数体 / 生成多項式 / 代数曲線 / ヤコビ多様体 |
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| Research Abstract |
We studied the Noether's Problem, which asks the rationality of the fixed field of the rational function field of several variables over a given field, with respect to a given finite subgroup G of the Cremona group. We solved this problem affirmatively in the case where G is one of the transitive permutation groups of degree six, and obtained the explicit description of the fixed field as expected. The results are now being collected and prepared in some papers, although it will take some time before the completion. During the period of the research, we had in each year a workshop entitled as "Galois theory and related topics", and discussed the various related problems.. They were held in the university of Yamagata (2007), Tokushima (2008), and Kanazawa (2009). We also had a conference on number theory each year at Waseda university and communicated with many experts of this subject, including those from foreign countries.
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Research Products
(42 results)
