List of algebraic number theory topics

This is a list of algebraic number theory topics, by Wikipedia page.

• Gaussian integer, Gaussian rational
• Quadratic field
• Algebraic number field
  • Dedekind domain
• Global field
• Ideal class group
  • Class number problem for imaginary quadratic fields
  • Stark-Heegner theorem
  • Heegner number
  • Ankeny-Artin-Chowla congruence
• Root of unity
  • Gaussian period, Gauss sum
  • Chowla-Mordell theorem
  • Cyclotomic field
    • Kronecker-Weber theorem
    • Herbrand-Ribet theorem
  • Number-theoretic transform
• Dirichlet's unit theorem
• Discriminant
• Ramification
• Different ideal
• Splitting of prime ideals in Galois extensions, Decomposition group, inertia group
• Frobenius automorphism
• Chebotarev's density theorem
• Abelian extension
• Quadratic reciprocity
• Class field theory
  • Local classfield theory
  • Takagi existence theorem
  • Hasse norm theorem
  • complex multiplication
    • Abelian variety of CM-type
• Normal integral basis
  • Hilbert-Speiser theorem
• Totally real field
• Chowla-Selberg formula
• P-adic number
  • P-adic analysis, Mahler's theorem
  • Local analysis
• Local field
• Adele ring
  • Idele group
  • Idele class group
  • Adelic algebraic group
• Hasse principle
  • Hasse-Minkowski theorem
• Hasse-Weil zeta function
• Galois module
• Galois cohomology
  • Brauer group
• Iwasawa theory
• Euler system