Module

ActualFiniteTameGroups.lean

Nyll.EtaleFundamentalGroups.Inertia.ActualFiniteTameGroups
2 declarations indexed from sourceView source ↗

Inertia and tame roots at finite stages

Defines the intrinsic finite normalization inertia group and the full residue-root group of its tame degree.

Declarations

EtaleFundamentalGroups.Inertia.actualFiniteStageInertiaGroup

The actual finite ideal-inertia group in its intrinsic normalization presentation.

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
variable (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)) [Q.IsMaximal]
def actualFiniteStageInertiaGroup (E : FiniteGaloisIntermediateField K L) : GrpCat.{w}
EtaleFundamentalGroups.Inertia.actualFiniteStageTameRootsGroup

The full actual residue-root group of the same original finite tame degree.

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
variable (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)) [Q.IsMaximal]
def actualFiniteStageTameRootsGroup (E : FiniteGaloisIntermediateField K L) : GrpCat.{w}