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

    • 田谷, 久雄 タヤ, ヒサオ

書誌事項

タイトル

Finiteness of Iwasawa modules of real abelian number fields

タイトル別名

実アーベル体の岩澤加群の有限性

著者名

田谷, 久雄

著者別名

タヤ, ヒサオ

学位授与大学

早稲田大学

取得学位

博士 (理学)

学位授与番号

甲第1116号

学位授与年月日

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

  1. Contents / p3 (0004.jp2)
  2. Acknowledgements / p2 (0003.jp2)
  3. Introduction / p1 (0006.jp2)
  4. Chapter1.Cyclotomic[数式]-extensions of real quadratic fields in which p splits / p4 (0009.jp2)
  5. 1.1 Invariants[数式]and[数式] / p5 (0010.jp2)
  6. 1.2 Ambiguous class groups, unit groups and[数式] / p7 (0012.jp2)
  7. 1.3 Ambiguous p-class groups, p-unit groups and[数式] / p11 (0016.jp2)
  8. 1.4 Remark on the p-adic L-function / p13 (0018.jp2)
  9. Chapter2.Iwasawa[数式]-invariants of real quadratic fields in which p splits / p15 (0020.jp2)
  10. 2.1 Two main theorems on Greenberg's conjecture / p16 (0021.jp2)
  11. 2.2 The growth of Dn and[数式]and[数式] / p19 (0024.jp2)
  12. 2.3 Proof of the first main theorem / p22 (0027.jp2)
  13. 2.4 Proof of the second main theorem / p24 (0029.jp2)
  14. 2.5 Miscellaneous criteria for Greenberg's conjecture / p25 (0030.jp2)
  15. 2.6 Additional remarks on the growth of Dn,and[数式]and[数式] / p28 (0033.jp2)
  16. Chapter3.Computation of Z₃-invariants of real quadratic fields in which p=3 splits / p35 (0040.jp2)
  17. 3.1 Computation of n₀, n₁ and n₂ / p35 (0040.jp2)
  18. 3.2 Computation of n₀⁽¹⁾and n₂⁽¹⁾for p=3 / p37 (0042.jp2)
  19. 3.3 Numerical examples with λ₃=0 / p38 (0043.jp2)
  20. 3.4 Probabilistic investigation on n₁ and n₂ / p43 (0048.jp2)
  21. Table3.1 All m's satisfying A₀≠D₀ or n₀≥2:1<m<10000 / p45 (0050.jp2)
  22. Tables3.2~3.4 The case of n₁=n₂=3,4 and 5 for p=3:10000<m / p50 (0055.jp2)
  23. Tables3.5~3.7 The number of a pair of n₁ and n₂ for p=3, 5 and 7 / p51 (0056.jp2)
  24. Chapter4.Iwasawa λ-invariants of real abelian number fields / p52 (0057.jp2)
  25. 4.1 A criterion for Greenberg's conjecture:A real abelian case / p52 (0057.jp2)
  26. 4.2 A criterion tor Greenberg's conjecture:A real quadratic case / p56 (0061.jp2)
  27. 4.3 Numerical examples with λ₃=0 in the case of real quadratic fields in which p=3 does not split / p59 (0064.jp2)
  28. Table4.1 All m's with m≡2(mod 3),A₀≠1 and[数式] / p64 (0069.jp2)
  29. Table4.2 All m's with m≡0(mod 3),A₀≠1 and[数式] / p66 (0071.jp2)
  30. Appendix A.Another proof of a special case of Corollary 2.7 / p68 (0073.jp2)
  31. A.1 Results and proofs / p68 (0073.jp2)
  32. Appendix B.Iwasawa modules for a prime p in a cyclic p-extension / p70 (0075.jp2)
  33. B.1 A main theorem / p70 (0075.jp2)
  34. B.2 Some lemmas concerning Galois cohomology groups / p71 (0076.jp2)
  35. B.3 Proof of our main theorem / p73 (0078.jp2)
  36. Appendix C.Iwasawa λ₂-invariants of certain families of real quadratic fields / p75 (0080.jp2)
  37. C.1 Statement of results / p75 (0080.jp2)
  38. C.2 Proof of our results / p76 (0081.jp2)
  39. References / p78 (0083.jp2)
  40. List of papers by Hisao Taya / p82 (0087.jp2)
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各種コード

  • NII論文ID(NAID)
    500000132394
  • NII著者ID(NRID)
    • 8000000967010
  • DOI(NDL)
  • 本文言語コード
    • eng
  • NDL書誌ID
    • 000000296708
  • データ提供元
    • 機関リポジトリ
    • NDL-OPAC
    • NDLデジタルコレクション
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