ClassFieldTheory.inverseHerbrandFunction_herbrandFunction
The inverse public Herbrand function recovers every real lower index.
Source context 5 commands
Surrounding namespaces, section variables, and local commands at this declaration.
noncomputable section
namespace ClassFieldTheory
open LocalFieldTheory
open RamificationTheory.LocalField
open RamificationTheory.HilbertRamification.HigherLean source · statement
theorem inverseHerbrandFunction_herbrandFunction
(K L : Type) [Field K] [Field L] [Algebra K L]
[FiniteDimensional K L] [IsAbelianGalois K L]
[ValuativeRel K] [TopologicalSpace K]
[IsNonarchimedeanLocalField K]
[ValuativeRel L] [TopologicalSpace L]
[IsNonarchimedeanLocalField L]
[Valuation.HasExtension (ValuativeRel.valuation K) (ValuativeRel.valuation L)]
(s : ℝ) :
inverseHerbrandFunction K L
(ClassFieldTheory.herbrandFunction K
(ValuativeRel.valuation L).valuationSubring s) = s