Module

NormalizationGaloisSurjectivity.lean

Nyll.SchemeTheory.Normalization.NormalizationGaloisSurjectivity
1 declaration indexed from sourceView source ↗

Surjectivity of native normalization automorphisms

Every intrinsic coefficient automorphism is induced by an automorphism of the finite fraction-field extension.

Declarations

SchemeTheory.normalizationGaloisGroupMap_surjective

The prescribed native finite normalization group map is onto the intrinsic coefficient automorphism group. The actual fraction-extension producer constructs its preimages.

Source context 3 commands

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

noncomputable section
namespace SchemeTheory
universe u v w
theorem normalizationGaloisGroupMap_surjective
    (A : Type u) (K : Type v) (F : Type w)
    [CommRing A] [Field K] [Field F]
    [Algebra A K] [IsFractionRing A K]
    [Algebra K F] [Algebra A F] [IsScalarTower A K F]
    [FiniteDimensional K F] :
    Function.Surjective (normalizationGaloisGroupMap A K F).hom