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Mathematical Sciences Classification System

11Rxx - Algebraic number theory: global fields
{For complex multiplication, see 11G15}

• 11R04
  Algebraic numbers; rings of algebraic integers
• 2
  11R06
  PV-numbers and generalizations; other special algebraic numbers; Mahler measure
• 11R09
  Polynomials (irreducibility, etc.)
• 2
  11R11
  Quadratic extensions
• 2
  11R16
  Cubic and quartic extensions
• 1
  11R18
  Cyclotomic extensions
• 11R20
  Other abelian and metabelian extensions
• 11R21
  Other number fields
• 3
  11R23
  Iwasawa theory
• 1
  11R27
  Units and factorization
• 4
  11R29
  Class numbers, class groups, discriminants
• 12
  11R32
  Galois theory
• 1
  11R33
  Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]
• 5
  11R34
  Galois cohomology [See also 12Gxx, 19A31]
• 9
  11R37
  Class field theory
• 9
  11R39
  Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
• 5
  11R42
  Zeta functions and $L$-functions of number fields [See also 11M41, 19F27]
• 1
  11R44
  Distribution of prime ideals [See also 11N05]
• 11R45
  Density theorems
• 11R47
  Other analytic theory [See also 11Nxx]
• 3
  11R52
  Quaternion and other division algebras: arithmetic, zeta functions
• 11R54
  Other algebras and orders, and their zeta and $L$-functions [See also 11S45, 16Hxx, 16Kxx]
• 1
  11R56
  Adèle rings and groups
• 8
  11R58
  Arithmetic theory of algebraic function fields [See also 14-XX]
• 11R60
  Cyclotomic function fields (class groups, Bernoulli objects, etc.)
• 11R65
  Class groups and Picard groups of orders
• 1
  11R70
  $K$-theory of global fields [See also 19Fxx]
• 1
  11R80
  Totally real fields [See also 12J15]
• 11R99
  None of the above, but in this section