EtaleFundamentalGroups.Inertia.actualTameCoordinate_conjugate_scalar
Source context 3 commands
Surrounding namespaces, section variables, and local commands at this declaration.
namespace EtaleFundamentalGroups.Inertia
open SchemeTheory
universe u v wLean source · statement
theorem actualTameCoordinate_conjugate_scalar
(A : Type u) (K : Type v) (L : Type w)
[CommRing A] [IsDomain A] [IsDiscreteValuationRing A]
[Field K] [Field L] [Algebra A K] [IsFractionRing A K]
[Algebra K L] [Algebra A L] [IsScalarTower A K L] [IsGalois K L]
(Q : Ideal (normalizationCommAlgCat A L).carrier) [Q.IsMaximal]
(n : Subtype (actualFiniteTameDegreeSet A K L Q))
(d : (normalizationDecompositionGroup A K L Q).carrier)
(σ : (actualNormalizationInertiaGroup A K L Q).carrier) :
((actualTameCoordinate A K L Q n).toFun
(originalFiniteNormalizationInertiaConjugate A K L Q d σ)).val.val =
((actualNormalizationQuotientAction A K L Q).toFun d).toFun
((actualTameCoordinate A K L Q n).toFun σ).val.val