11Rxx

11P | 11 | 11S

Algebraic number theory: global fields

{For complex multiplication, see 11G15}

11R04Algebraic numbers; rings of algebraic integers
11R06PV-numbers and generalizations; other special algebraic numbers
11R09Polynomials (irreducibility, etc.)
11R11Quadratic extensions
11R16Cubic and quartic extensions
11R18Cyclotomic extensions
11R20Other abelian and metabelian extensions
11R21Other number fields
11R23Iwasawa theory
11R27Units and factorization
11R29Class numbers, class groups, discriminants
11R32Galois theory
11R33Integral representations related to algebraic numbers; Galois module structure of rings of integers
[See also 20C10]
11R34Galois cohomology
[See also 12Gxx, 16H05, 19A31]
11R37Class field theory
11R39Langlands-Weil conjectures, nonabelian class field theory
[See also 11Fxx, 22E55]
11R42Zeta functions and L-functions of number fields
[See also 11M41, 19F27]
11R44Distribution of prime ideals
[See also 11N05]
11R45Density theorems
11R47Other analytic theory
[See also 11Nxx]
11R52Quaternion and other division algebras: arithmetic, zeta functions
11R54Other algebras and orders, and their zeta and L-functions
[See also 11S45, 16H05, 16Kxx]
11R56Adèle rings and groups
11R58Arithmetic theory of algebraic function fields
[See also 14-XX]
11R60Cyclotomic function fields (class groups, Bernoulli objects, etc.)
11R65Class groups and Picard groups of orders
11R70K-theory of global fields
[See also 19Fxx]
11R80Totally real and totally positive fields
[See also 12J15]
11R99None of the above, but in this section