Finiteness of Iwasawa modules of real abelian number fields 実アーベル体の岩澤加群の有限性
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著者
書誌事項
- タイトル
-
Finiteness of Iwasawa modules of real abelian number fields
- タイトル別名
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実アーベル体の岩澤加群の有限性
- 著者名
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田谷, 久雄
- 著者別名
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タヤ, ヒサオ
- 学位授与大学
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早稲田大学
- 取得学位
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博士 (理学)
- 学位授与番号
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甲第1116号
- 学位授与年月日
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1996-02-08
注記・抄録
博士論文
制度:新 ; 文部省報告番号:甲1116号 ; 学位の種類:博士(理学) ; 授与年月日:1996-02-08 ; 早大学位記番号:新2271 ; 理工学図書館請求番号:1940
目次
- Contents / p3 (0004.jp2)
- Acknowledgements / p2 (0003.jp2)
- Introduction / p1 (0006.jp2)
- Chapter1.Cyclotomic[数式]-extensions of real quadratic fields in which p splits / p4 (0009.jp2)
- 1.1 Invariants[数式]and[数式] / p5 (0010.jp2)
- 1.2 Ambiguous class groups, unit groups and[数式] / p7 (0012.jp2)
- 1.3 Ambiguous p-class groups, p-unit groups and[数式] / p11 (0016.jp2)
- 1.4 Remark on the p-adic L-function / p13 (0018.jp2)
- Chapter2.Iwasawa[数式]-invariants of real quadratic fields in which p splits / p15 (0020.jp2)
- 2.1 Two main theorems on Greenberg's conjecture / p16 (0021.jp2)
- 2.2 The growth of Dn and[数式]and[数式] / p19 (0024.jp2)
- 2.3 Proof of the first main theorem / p22 (0027.jp2)
- 2.4 Proof of the second main theorem / p24 (0029.jp2)
- 2.5 Miscellaneous criteria for Greenberg's conjecture / p25 (0030.jp2)
- 2.6 Additional remarks on the growth of Dn,and[数式]and[数式] / p28 (0033.jp2)
- Chapter3.Computation of Z₃-invariants of real quadratic fields in which p=3 splits / p35 (0040.jp2)
- 3.1 Computation of n₀, n₁ and n₂ / p35 (0040.jp2)
- 3.2 Computation of n₀⁽¹⁾and n₂⁽¹⁾for p=3 / p37 (0042.jp2)
- 3.3 Numerical examples with λ₃=0 / p38 (0043.jp2)
- 3.4 Probabilistic investigation on n₁ and n₂ / p43 (0048.jp2)
- Table3.1 All m's satisfying A₀≠D₀ or n₀≥2:1<m<10000 / p45 (0050.jp2)
- Tables3.2～3.4 The case of n₁=n₂=3,4 and 5 for p=3:10000<m / p50 (0055.jp2)
- Tables3.5～3.7 The number of a pair of n₁ and n₂ for p=3, 5 and 7 / p51 (0056.jp2)
- Chapter4.Iwasawa λ-invariants of real abelian number fields / p52 (0057.jp2)
- 4.1 A criterion for Greenberg's conjecture:A real abelian case / p52 (0057.jp2)
- 4.2 A criterion tor Greenberg's conjecture:A real quadratic case / p56 (0061.jp2)
- 4.3 Numerical examples with λ₃=0 in the case of real quadratic fields in which p=3 does not split / p59 (0064.jp2)
- Table4.1 All m's with m≡2(mod 3),A₀≠1 and[数式] / p64 (0069.jp2)
- Table4.2 All m's with m≡0(mod 3),A₀≠1 and[数式] / p66 (0071.jp2)
- Appendix A.Another proof of a special case of Corollary 2.7 / p68 (0073.jp2)
- A.1 Results and proofs / p68 (0073.jp2)
- Appendix B.Iwasawa modules for a prime p in a cyclic p-extension / p70 (0075.jp2)
- B.1 A main theorem / p70 (0075.jp2)
- B.2 Some lemmas concerning Galois cohomology groups / p71 (0076.jp2)
- B.3 Proof of our main theorem / p73 (0078.jp2)
- Appendix C.Iwasawa λ₂-invariants of certain families of real quadratic fields / p75 (0080.jp2)
- C.1 Statement of results / p75 (0080.jp2)
- C.2 Proof of our results / p76 (0081.jp2)
- References / p78 (0083.jp2)
- List of papers by Hisao Taya / p82 (0087.jp2)
