EtaleFundamentalGroups.Inertia.actualFiniteTameCoordinate_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 actualFiniteTameCoordinate_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]
(E : FiniteGaloisIntermediateField K L)
(d : (normalizationDecompositionGroup A K L Q).carrier)
(σ : (actualNormalizationInertiaGroup A K L Q).carrier) :
((actualFiniteTameCoordinate A K L Q E).hom'.toFun
(originalFiniteNormalizationInertiaConjugate A K L Q d σ)).val.val =
(actualNormalizationResidueFieldMap A K L Q d).toFun
((actualFiniteTameCoordinate A K L Q E).hom'.toFun σ).val.val