代数数论主题列表

  • 高斯整数, 高斯有理数
  • 二次域 (Quadratic field)
  • 代数数域
    • 戴德金整環 (Dedekind domain)
  • Global field
  • 理想類群
    • Class number problem for imaginary quadratic fields
    • Stark-Heegner 定理
    • 黑格纳数
    • Ankeny-Artin-Chowla congruence
  • 单位根
    • 高斯周期, 高斯和
    • Chowla-Mordell 定理
    • 分圆域
      • 克罗内克-韦伯定理
      • Herbrand-Ribet 定理
    • 数论变换
  • 狄利克雷单位定理
  • 判别式
  • Ramification
  • Different ideal
  • Splitting of prime ideals in Galois extensions, Decomposition group, inertia group
  • 弗羅貝尼烏斯自同態 (Frobenius automorphism)
  • Chebotarev's density theorem
  • 阿贝尔扩张 (Abelian extension)
  • 二次互反律 (Quadratic reciprocity)
  • 類域論
    • 局部類域論
    • Takagi 存在性定理
    • 哈瑟範數定理
    • 複數乘法
  • 正規整基
    • Hilbert-Speiser 定理
  • 全實域
  • Chowla-Selberg 公式
  • P进数 (p-adic number)
    • P进数分析 (p-adic analysis), 马勒定理
    • 局部分析
  • 局部域
  • 賦值向量環
    • Idele group
    • Idele class group
    • Adelic algebraic group
  • 哈瑟原則
    • 哈瑟-闵可夫斯基定理
  • 伽罗瓦模
  • 伽羅瓦上同調
    • Brauer 群
  • 岩澤理论
  • 欧拉系统(英语:Euler system)

参见

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