Module

CommAlgIdealTameProperties.lean

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

Positivity and invertibility of intrinsic tame orders

Proves positivity of the intrinsic finite tame order and its invertibility in the original local coefficient ring under the stated hypotheses.

Declarations

EtaleFundamentalGroups.Inertia.commAlgIdealTameOrder_pos

Positivity for the intrinsic actual finite normalization action.

Source context 3 commands

Surrounding namespaces, section variables, and local commands at this declaration.

namespace EtaleFundamentalGroups.Inertia
universe u v
variable (A : Type u) [CommRing A] (B : CommAlgCat.{v} A)
  [IsDedekindDomain B] [Finite (B ≃ₐ[A] B)]
  (Q : Ideal B) [Q.IsPrime] (hQ : Q ≠ ⊥)
theorem commAlgIdealTameOrder_pos : 0 < commAlgIdealTameOrder A B Q hQ
EtaleFundamentalGroups.Inertia.commAlgIdealTameOrder_isUnit

Base invertibility for the intrinsic actual coefficient automorphisms.

Source context 3 commands

Surrounding namespaces, section variables, and local commands at this declaration.

namespace EtaleFundamentalGroups.Inertia
universe u v
variable (A : Type u) [CommRing A] (B : CommAlgCat.{v} A)
  [IsDedekindDomain B] [Finite (B ≃ₐ[A] B)]
  (Q : Ideal B) [Q.IsPrime] (hQ : Q ≠ ⊥)
theorem commAlgIdealTameOrder_isUnit [IsLocalRing A]
    [Q.LiesOver (IsLocalRing.maximalIdeal A)] :
    IsUnit (commAlgIdealTameOrder A B Q hQ : A)