| Project/Area Number |
20540013
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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 | Kanazawa University |
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Principal Investigator |
NOMURA Akito Kanazawa University, 機械工学系, 准教授 (00313700)
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| Co-Investigator(Kenkyū-buntansha) |
ITO Tatsuro 金沢大学, 数物科学系, 教授 (90015909)
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| Co-Investigator(Renkei-kenkyūsha) |
HIRABAYASHI Mikihito 金沢工業大学, 基礎教育部, 教授 (20167612)
KIMURA Iwao 富山大学, 理工学研究部, 准教授 (10313587)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | ガロアの逆問題 / 代数体の埋め込み問題 / 分岐 / 類数 / 類体塔 / イデアル類群 / 不分岐拡大 / 埋め込み問題 / 代数学 |
|---|
| Research Abstract |
Frohlich proved that for any p-group G, there exists a number field k and the unramified Galois extension K/k such that the Galois group is isomorphic to G. In Frohlich's method, the degree of the base field k is high in general. We wanted to reduce the degree of the base field k as much as possible. And we proved that the base field k can be chosen as elementary abelian p-extension over the rational number field. As a corollary of the theorem, we proved that there exists an elementary abelian p-extension such that the ideal class group contains an element of big order.
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