Category:Algebraic number theory

• Theorems in algebraic number theory (40 P)

A

• Algebraic numbers (3 C, 19 P)

C

• Class field theory (36 P)
• Cyclotomic fields (23 P)

F

• Finite fields (65 P)

I

• Integers (24 C, 450 P)

Z

• Zeta and L-functions (102 P)

• Algebraic number theory

*

• Abstract analytic number theory
• List of algebraic number theory topics

A

• Abelian extension
• Abhyankar's lemma
• Additive polynomial
• Adele ring
• Adelic algebraic group
• Algebraic function
• Algebraic number field
• Arithmetic and geometric Frobenius
• Arithmetic dynamics
• Arithmetic topology
• Artin's conjecture on primitive roots

B

• Basic Number Theory
• Biquadratic field
• Brauer group
• Brumer–Stark conjecture

C

• Carlitz exponential
• Class formation
• Class number formula
• Class number problem
• CM-field
• Compatible system of ℓ-adic representations
• Conductor of an abelian variety
• Conductor-discriminant formula
• Cubic field
• Cubic reciprocity
• Cyclotomic character
• Cyclotomic field
• Cyclotomic unit

D

• Dedekind domain
• Dedekind zeta function
• Dedekind–Kummer theorem
• Different ideal
• Discriminant
• Discriminant of an algebraic number field
• Drinfeld module

E

• E-function
• Eisenstein reciprocity
• Eisenstein sum
• Elementary number
• Elliptic Gauss sum
• Elliptic unit
• Equivariant L-function
• Euler system
• Explicit reciprocity law

F

• Field norm
• Finite extensions of local fields
• Fontaine's period rings
• Formal group law
• Fractional ideal
• Frobenius endomorphism
• Fundamental unit (number theory)

G

• Galois cohomology
• Galois extension
• Galois representation
• Genus character
• Global field
• Greenberg's conjectures
• Group cohomology

H

• Hasse invariant of an algebra
• Hasse principle
• Heegner number
• Heegner point
• Height function
• Herbrand quotient
• Hermite's problem
• Higher local field
• Hilbert's ninth problem
• Hilbert's twelfth problem

I

• Ideal (ring theory)
• Ideal class group
• Ideal norm
• Infrastructure (number theory)
• Integer

K

• Kummer theory
• Kummer–Vandiver conjecture

L

• Lazard's universal ring
• Leopoldt's conjecture
• List of number fields with class number one
• Local Euler characteristic formula
• Local field
• Local Fields
• Lubin–Tate formal group law

M

• Maillet's determinant
• Minkowski space (number field)
• Modular forms modulo p
• Modulus (algebraic number theory)
• Monogenic field

N

• Narrow class group
• Newton polygon
• Norm group

P

• P-adic Hodge theory
• P-adic valuation
• Parshin chain
• Perfectoid space
• Power residue symbol
• Profinite integer

Q

• Quadratic field
• Quadratic integer
• Quadratic reciprocity
• Proofs of quadratic reciprocity
• Quartic reciprocity

R

• Ramification (mathematics)
• Ramification group
• Rational reciprocity law
• Reciprocity law
• Regular prime
• Rigid analytic space
• Ring class field
• Ring of integers

S

• S-unit
• Serre's conjecture II
• Siegel G-function
• Skolem–Mahler–Lech theorem
• Splitting of prime ideals in Galois extensions
• Stark conjectures
• Stephens' constant
• Supersingular prime (algebraic number theory)

T

• Tamagawa number
• Tate duality
• Tate's thesis
• Totally imaginary number field
• Totally real number field
• Twisted polynomial ring

U

• Unique factorization domain
• Unit (ring theory)

W

• Waldspurger formula

Z

• Zahlbericht