Module

BigHilbertClassFieldUnique.lean

Nyll.ClassFieldTheory.Theorems.FrobeniusAndHilbertClassFields.BigHilbertClassFieldUnique
1 declaration indexed from sourceView source ↗

Uniqueness of the big Hilbert class field inside a separable closure

Maximality among finite-prime-unramified abelian extensions determines one intermediate field of the fixed separable closure.

Declarations

ClassFieldTheory.bigHilbertClassFields_eq

Two big Hilbert class fields inside the same separable closure are equal as intermediate fields.

Source context 3 commands

Surrounding namespaces, section variables, and local commands at this declaration.

noncomputable section
namespace ClassFieldTheory
universe u
theorem bigHilbertClassFields_eq
    (K : Type u) [Field K] [NumberField K]
    (E F : FiniteAbelianExtension K)
    (hE : IsBigHilbertClassField E)
    (hF : IsBigHilbertClassField F) :
    E.1 = F.1