11Rxx Algebraic number theory: global fields,

• 11R04 Algebraic numbers; rings of algebraic integers
• 11R06 PV-numbers and generalizations; other special algebraic numbers
• 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
• 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, 16H05, 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, 16H05, 16Kxx}
• 11R56 Adele rings and groups
• 11R58 Arithmetic theory of algebraic function fields, See also {14-XX}
• 11R65 Class groups and Picard groups of orders
• 11R70 $K$-theory of global fields, See also {19Fxx}
• 11R80 Totally real and totally positive fields, See also {12J15}
• 11R99 None of the above but in this section