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

{{DEFAULTSORT:Algebraic number theory topics}}

Category:Mathematics-related lists

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