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Conductor-discriminant formula : ウィキペディア英語版
Conductor-discriminant formula
In mathematics, the conductor-discriminant formula or Führerdiskriminantenproduktformel, introduced by for abelian extensions and by for Galois extensions, is a formula calculating the relative discriminant of a finite Galois extension L/K of local or global fields from the Artin conductors of the irreducible characters \mathrm(G) of the Galois group G = G(L/K).
== Statement ==
Let L/K be a finite Galois extension of global fields with Galois group G. Then the discriminant equals
:: \mathfrak_ = \prod_\mathfrak(\chi)^,
where \mathfrak(\chi) equals the global Artin conductor of \chi.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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