User:RobHar/Sandbox3

Basic notions

 * Algebraic number fields
 * Class groups
 * Primes and places
 * Unit groups
 * Discriminant of an algebraic number field
 * Conductor
 * Localization

Branches of algebraic number theory

 * Class field theory
 * Iwasawa theory
 * Galois representations
 * Arithmetic geometry

Major results

 * Finiteness of the class number
 * Dirichlet's unit theorem
 * Kronecker–Weber theorem
 * Artin reciprocity
 * Class number formula

Open questions

 * Non-abelian class field theory
 * Special values of L-functions
 * Birch-Swinnerton-Dyer
 * Bloch-Kato
 * Iwasawa "main conjectures"