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 ***Stickelberger s theorem ***Kronecker-Weber theorem ***Herbrand-Ribet theorem ***Vandiver s conjecture **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