List of algebraic number theory topics
 | This article may be confusing or unclear to readers. (April 2009) |
This is a list of algebraic number theory topics.
Basic topics[edit]
These topics are basic to the field, either as prototypical examples, or as basic objects of study.
- Algebraic number field
- Quadratic reciprocity
- Ideal class group
- Dirichlet's unit theorem
- Discriminant of an algebraic number field
- Ramification (mathematics)
- Root of unity
- Gaussian period
Important problems[edit]
General aspects[edit]
- 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
- Adele ring
- Idele group
- Idele class group
- Adelic algebraic group
- Global field
- Hasse principle
- Galois module
- Galois cohomology
Class field theory[edit]
- 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[edit]
- Iwasawa theory
- Herbrand–Ribet theorem
- Vandiver's conjecture
- Stickelberger's theorem
- Euler system
- p-adic L-function