| Project/Area Number |
15K04791
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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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| Research Field |
Algebra
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| Research Institution | Chiba Institute of Technology |
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Principal Investigator |
ITOH Tsuyoshi 千葉工業大学, 社会システム科学部, 教授 (80339689)
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| Co-Investigator(Kenkyū-buntansha) |
藤井 俊 島根大学, 学術研究院教育学系, 准教授 (20386618)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 岩澤理論 / 馴分岐拡大 / 岩澤加群 |
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| Outline of Final Research Achievements |
We studied "tamely ramified Iwasawa modules" for Z_p-extensions (or multiple Z_p-extensions) of algebraic number fields. In particular, we obtained several partial results for the question to when it has a non-trivial finite submodule.
We also studied the structure of the Galois group of unramified (or tamely ramified) pro-p extensions over the cyclotomic Z_p-extension field of an algebraic number field.
In addition, a result concerning the structure of the Galois group of certain tamely ramified abelian 3-extensions over the initial layer of the anti-cyclotomic Z_3-extension of an imaginary quadratic field was obtained.
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| Academic Significance and Societal Importance of the Research Achievements |
代数体のZ_p拡大（もしくはmultiple Z_p拡大）上のある種のpro-p拡大のガロア群の構造に関して、従来は知られていなかった新しい研究成果を得ることができた。特に、Z_p拡大の馴分岐岩澤加群の有限部分加群についての成果たちは、今後の研究において重要な役割を果たす可能性がある。また、得られた成果のうちのいくつかは、代数体の「非アーベル岩澤理論」の進展にいくらか寄与するものであると見ることができる。
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