ClassFieldTheory.upperRamificationGroup_herbrandFunction
The upper group at the Herbrand image of a real lower index is exactly the corresponding real lower group of the canonical valuation ring.
Source context 1 command
Surrounding namespaces, section variables, and local commands at this declaration.
namespace ClassFieldTheoryLean source · statement
theorem upperRamificationGroup_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) :
upperRamificationGroup K L
(herbrandFunction K (ValuativeRel.valuation L).valuationSubring s) =
realLowerRamificationGroup K
(ValuativeRel.valuation L).valuationSubring s