Module

NormalizationQuotientRoots.lean

Nyll.EtaleFundamentalGroups.Inertia.NormalizationQuotientRoots
1 declaration indexed from sourceView source ↗

The canonical quotient comparison on roots

Restricts the already constructed maximal-quotient residue equivalence to roots. Both the scalar evaluation and inverse needed for surjectivity use this same equivalence.

Declarations

EtaleFundamentalGroups.Inertia.normalizationQuotientRootsEquiv

The SAME maximal quotient/residue comparison, restricted to roots.

Source context 4 commands

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

noncomputable section
namespace EtaleFundamentalGroups.Inertia
universe u v
attribute [local instance] Ideal.Quotient.field
def normalizationQuotientRootsEquiv
    (A : Type u) (L : Type v) [CommRing A] [CommRing L] [Algebra A L]
    (Q : Ideal (SchemeTheory.normalizationCommAlgCat A L).carrier) [Q.IsMaximal]
    (n : ℕ) : (normalizationRootsGroup A L Q n).carrier ≃*
      rootsOfUnity n ((SchemeTheory.normalizationCommAlgCat A L).carrier ⧸ Q)