11Rxx Algebraic number theory: global fields (For complex multiplication, see 11G15)
 11R04 Algebraic numbers; rings of algebraic integers
 11R06 PVnumbers 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
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 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 LanglandsWeil conjectures, nonabelian class field theory [See also 11Fxx, 22E55]
 11R42 Zeta functions and Lfunctions 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 Lfunctions [See also 11S45, 16Hxx, 16Kxx]
 11R56 Adèle rings and groups
 11R58 Arithmetic theory of algebraic function fields [See also 14XX]
 11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)
 11R65 Class groups and Picard groups of orders
 11R70 Ktheory of global fields [See also 19Fxx]
 11R80 Totally real fields [See also 12J15]
 11R99 None of the above, but in this section