## 11Rxx Algebraic number theory: global fields (For complex multiplication, see 11G15)

- 11R04 Algebraic numbers; rings of algebraic integers
- 11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure
- 11R09 Polynomials (irreducibility, etc.)
- 11R11 Quadratic extensions
- 11R16 Cubic and quartic extensions
- 11R18 Cyclotomic extensions
- 11R20 Other abelian and metabelian extensions
- 11R21 Other number fields
- 11R23 Iwasawa theory
- 11R27 Units and factorization
- 11R29 Class numbers, class groups, discriminants (1)
- 11R32 Galois theory
- 11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers [See also 20C10]
- 11R34 Galois cohomology [See also 12Gxx, 19A31]
- 11R37 Class field theory
- 11R39 Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
- 11R42 Zeta functions and L-functions of number fields [See also 11M41, 19F27]
- 11R44 Distribution of prime ideals [See also 11N05]
- 11R45 Density theorems
- 11R47 Other analytic theory [See also 11Nxx]
- 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]
- 11R56 Adèle rings and groups
- 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
- 11R70 K-theory of global fields [See also 19Fxx]
- 11R80 Totally real fields [See also 12J15]
- 11R99 None of the above, but in this section