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]
  • 8
    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
  • 7
    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

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