Module

IsAbelianConductorUnique.lean

Nyll.ClassFieldTheory.Theorems.ConductorsAndRayClassFields.IsAbelianConductorUnique
1 declaration indexed from sourceView source ↗

Uniqueness of the conductor

A finite abelian extension has at most one modulus that characterizes exactly the ray class fields containing it.

Declarations

ClassFieldTheory.IsAbelianConductor.unique

The least modulus characterized by ray-class-field containment is unique.

Source context 2 commands

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

namespace ClassFieldTheory
universe u v
theorem IsAbelianConductor.unique
    {K : Type u} [Field K] [NumberField K]
    {L : Type v} [Field L] [NumberField L] [Algebra K L]
    {c d : RayClassModulus K}
    (hc : IsAbelianConductor K L c)
    (hd : IsAbelianConductor K L d) : c = d