EtaleFundamentalGroups.Inertia.finiteAbsoluteNormalizationAlgebra_isDedekindDomain
The native actual finite normalization is Dedekind. The finite field's inherited structures are supplied before this original-data proof.
Source context 2 commands
Surrounding namespaces, section variables, and local commands at this declaration.
namespace EtaleFundamentalGroups.Inertia
universe u v wLean source · statement
theorem finiteAbsoluteNormalizationAlgebra_isDedekindDomain
(A : Type u) (K : Type v) (L : Type w)
[CommRing A] [IsDedekindDomain A] [Field K] [Field L]
[Algebra A K] [IsFractionRing A K]
[Algebra K L] [Algebra A L] [IsScalarTower A K L] [IsGalois K L]
(E : FiniteGaloisIntermediateField K L) :
IsDedekindDomain (finiteAbsoluteNormalizationAlgebra A K L E)