Conductor-discriminant formula

In mathematics, the conductor-discriminant formula or Führerdiskriminantenproduktformel, introduced by Hasse (1926, 1930) for abelian extensions and by Artin (1931) for Galois extensions, is a formula calculating the relative discriminant of a finite Galois extension ${\displaystyle L/K}$ of local or global fields from the Artin conductors of the irreducible characters ${\displaystyle \mathrm {Irr} (G)}$ of the Galois group ${\displaystyle G=G(L/K)}$.