List of algebraic number theory topics
This is a list of algebraic number theory topics.Basic topics
These topics are basic to the field, either as prototypical examples, or as basic objects of study.
- Algebraic number field
- *Gaussian integer, Gaussian rational
- *Quadratic field
- *Cyclotomic field
- *Cubic field
- *Biquadratic field
- Quadratic reciprocity
- Ideal class group
- Dirichlet's unit theorem
- Discriminant of an algebraic number field
- Ramification
- Root of unity
- Gaussian period
Important problems
- Fermat's last theorem
- Class number problem for imaginary quadratic fields
- *Stark–Heegner theorem
- **Heegner number
- Langlands program
General aspects
- Different ideal
- Dedekind domain
- Splitting of prime ideals in Galois extensions
- Decomposition group
- Inertia group
- Frobenius automorphism
- Chebotarev's density theorem
- Totally real field
- Local field
- *p-adic number
- *p-adic analysis
- Adele ring
- Idele group
- Idele class group
- Adelic algebraic group
- Global field
- Hasse principle
- *Hasse–Minkowski theorem
- Galois module
- Galois cohomology
- *Brauer group
- Class field theory
- Abelian extension
- Kronecker–Weber theorem
- Hilbert class field
- Takagi existence theorem
- Hasse norm theorem
- Artin reciprocity
- Local class field theory
Iwasawa theory
- Iwasawa theory
- Herbrand–Ribet theorem
- Vandiver's conjecture
- Stickelberger's theorem
- Euler system
- p-adic L-function
Arithmetic geometry
- Arithmetic geometry
- Complex multiplication
- Abelian variety of CM-type
- *Chowla–Selberg formula
- Hasse–Weil zeta function
