Category:Algebraic number theory

• ► Theorems in algebraic number theory‎ (39 P)

A

• ► Algebraic numbers‎ (3 C, 23 P)

C

• ► Class field theory‎ (36 P)
• ► Cyclotomic fields‎ (25 P)

F

• ► Finite fields‎ (63 P)

I

• ► Integers‎ (14 C, 410 P)

Z

• ► Zeta and L-functions‎ (101 P)

• Algebraic number theory (computing)

*

• Abstract analytic number theory (computing)
• List of algebraic number theory topics (computing)

A

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

B

• Biquadratic field (computing)
• Brauer group (computing)
• Brumer–Stark conjecture (computing)

C

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

D

• Dedekind domain (computing)
• Dedekind zeta function (computing)
• Different ideal (computing)
• Discriminant (computing)
• Discriminant of an algebraic number field (computing)
• Drinfeld module (computing)

E

• Eisenstein reciprocity (computing)
• Eisenstein sum (computing)
• Elementary number (computing)
• Elliptic Gauss sum (computing)
• Elliptic unit (computing)
• Equivariant L-function (computing)
• Euler system (computing)
• Explicit reciprocity law (computing)
• Extension and contraction of ideals (computing)

F

• Proofs of Fermat's theorem on sums of two squares (computing)
• Field norm (computing)
• Finite extensions of local fields (computing)
• Fontaine's period rings (computing)
• Formal group law (computing)
• Fractional ideal (computing)
• Frobenius endomorphism (computing)
• Fundamental discriminant (computing)
• Fundamental unit (number theory) (computing)

G

• Galois cohomology (computing)
• Galois extension (computing)
• Galois module (computing)
• Genus character (computing)
• Global field (computing)
• Greenberg's conjectures (computing)
• Group cohomology (computing)

H

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

I

• Ideal (ring theory) (computing)
• Ideal class group (computing)
• Ideal norm (computing)
• Integer (computing)

K

• Kummer theory (computing)

L

• Lazard's universal ring (computing)
• Leopoldt's conjecture (computing)
• Local Euler characteristic formula (computing)
• Local field (computing)
• Local Fields (computing)
• Lubin–Tate formal group law (computing)

M

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

N

• Narrow class group (computing)
• Newton polygon (computing)
• Norm group (computing)

P

• P-adic Hodge theory (computing)
• P-adic order (computing)
• Parshin chain (computing)
• Perfectoid space (computing)
• Power residue symbol (computing)
• Profinite integer (computing)

Q

• Quadratic field (computing)
• Quadratic integer (computing)
• Quadratic reciprocity (computing)
• Proofs of quadratic reciprocity (computing)
• Quartic reciprocity (computing)

R

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

S

• S-unit (computing)
• Serre's conjecture II (algebra) (computing)
• Skolem–Mahler–Lech theorem (computing)
• Splitting of prime ideals in Galois extensions (computing)
• Stark conjectures (computing)
• Stephens' constant (computing)
• Supersingular prime (algebraic number theory) (computing)
• Supersingular prime (for an elliptic curve) (computing)

T

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

U

• Unique factorization domain (computing)
• Unit (ring theory) (computing)

W

• Waldspurger formula (computing)

Z

• Zahlbericht (computing)