List of algebraic number theory topics

This is a list of algebraic number theory 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 (mathematics)
• Root of unity
• Gaussian period

• Fermat's last theorem
• Class number problem for imaginary quadratic fields
  • Stark–Heegner theorem
    • Heegner number
• Langlands program

• 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
• Herbrand–Ribet theorem
• Vandiver's conjecture
• Stickelberger's theorem
• Euler system
• p-adic L-function

• Arithmetic geometry
• Complex multiplication
• Abelian variety of CM-type
  • Chowla–Selberg formula
• Hasse–Weil zeta function

This article does not cite any external source. HandWiki requires at least one external source. See citing external sources. Please help improve this article. Unsourced material may be removed in future. Find sources: "List of algebraic number theory topics" – news · newspapers · books · scholar · JSTOR (2021) (Learn how and when to remove this template message)

0.00 (0 votes) Original source: https://en.wikipedia.org/wiki/List of algebraic number theory topics. Read more