Neha Patil (Editor)

List of algebraic number theory topics

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This is a list of algebraic number theory topics.

Contents

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 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

    • Arithmetic geometry

  • Arithmetic geometry
  • Complex multiplication
  • Abelian variety of CM-type
  • Chowla–Selberg formula
  • Hasse–Weil zeta function

    • References

    List of algebraic number theory topics Wikipedia
    (Text) CC BY-SA


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