EtaleFundamentalGroups.Inertia.actualFiniteQuotientTameCoordinate
The SAME finite canonical coordinate, in the literal quotient root group.
Source context 5 commands
Surrounding namespaces, section variables, and local commands at this declaration.
noncomputable section
namespace EtaleFundamentalGroups.Inertia
open SchemeTheory
universe u v w
attribute [local instance] Ideal.Quotient.fieldLean source · statement
def actualFiniteQuotientTameCoordinate
(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) :
(actualNormalizationInertiaGroup A K L Q).carrier →*
rootsOfUnity (actualFiniteStageTameOrder A K L Q E)
((normalizationCommAlgCat A L).carrier ⧸ Q)