Algebraic number theory

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Number field Ring of integers Class groups Unit Ramification Local field Abhyankars lemma Additive polynomial Adele ring Adelic algebraic group Algebraic number field Arithmetic and geometric frobenius Biquadratic field Brauer group Carlitz exponential Class number formula Class number problem Class numbers of imaginary quadratic fields Cm field Compatible system of l adic representations Contou carrere symbol Cubic field Cyclotomic character Cyclotomic field Cyclotomic polynomial Cyclotomic unit Dedekind domain Dedekind kummer theorem Deformation ring Different ideal Diophantine dimension Discriminant of an algebraic number field Drinfeld module Eisenstein sum Eisensteins theorem Elliptic unit Equivariant tamagawa number conjecture Euler system Field norm Finite extensions of local fields Finite field Fontaine mazur conjecture Formal group law Fractional ideal Frobenius endomorphism Fundamental unit number theory Galois module Galois representation Genus character Global field Golden field Harans diamond theorem Hasse invariant of an algebra Heegner number Herbrand quotient Hermites problem Higher local field Hilbertian field Hilberts irreducibility theorem Hilberts ninth problem Hilberts twelfth problem Ideal class group Ideal norm Ideal number Idele group Imaginary quadratic field Infrastructure number theory Inverse galois problem Kummer theory Lazards universal ring Local euler characteristic formula Lubin tate formal group law Maillets determinant Minimal polynomial of 2cos 2pi n Minkowski space number field Modulus algebraic number theory Monogenic field Narrow class group Newton polygon Noncommutative unique factorization domain Norm group Parshin chain Prime ideal Profinite integer Quadratic field Quadratic integer Quasi algebraic closure Quasi algebraically closed field Ramification group Ramification theory Regular prime Root of unity Serres conjecture ii Splitting of prime ideals in galois extensions Stickelbergers theorem Supersingular prime algebraic number theory Tamagawa number Tate duality Thin set serre Totally imaginary number field Totally real number field Tsen rank Twisted polynomial ring Unique factorization domain Weil conjecture on tamagawa numbers Abelian number field Adele group Algebraic diophantine equations Binary p adic group Diophantine approximation metric theory of Diophantine approximation problems of effective Diophantine equations solvability problem of Diophantine predicate Diophantine problems of additive type Divisor class group Euler systems for number fields Gamma invariant in the theory of modular forms Height in diophantine geometry Hyper elliptic curve Lie group p adic Non abelian number field P adically closed field Ramification theory of valued fields Regulator of an algebraic number field Transference theorem in diophantine approximation

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