11Rxx

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11Rxx Algebraic number theory: global fields {For complex multiplication, see 11G15} {Info & Stats}

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• 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
• 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, 16H0516Hxx, 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 and totally positive fields [See also 12J15]
• 11R99 None of the above, but in this section