Editing List of algebraic number theory topics

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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 (mathematics)]]
*[[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 number]]
**[[P-adic analysis|''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==
*[[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|''p''-adic ''L''-function]]

==Arithmetic geometry==
*[[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]]
[[Category:Algebraic number theory|*]]