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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Etale.iff_flat_and_formallyUnramified

∀ {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y},
  AlgebraicGeometry.Etale f ↔
    AlgebraicGeometry.Flat f ∧ AlgebraicGeometry.FormallyUnramified f ∧ AlgebraicGeometry.LocallyOfFinitePresentation f
Defined in
Mathlib.AlgebraicGeometry.Morphisms.Etale
Cited by
1 results in Mathlib
Foundations
Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
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AlgebraicGeometry.Etale.of_formallyUnramified_of_flat · cited by 0Etale.of_formallyUnramifi…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.PresheafedSpace.Hom.base · cited by 1135Hom.baseAlgebraicGeometry.LocallyRingedSpace.Hom.toHom · cited by 995Hom.toHomAlgebraicGeometry.Scheme.Hom.toLRSHom' · cited by 895Hom.toLRSHom'TopologicalSpace.Opens.map · cited by 645Opens.mapCommRingCat.Hom.hom · cited by 432Hom.homAlgebraicGeometry.IsAffineOpen · cited by 222AlgebraicGeometry.IsAffin…AlgebraicGeometry.Scheme.Hom.appLE · cited by 138Hom.appLERingHom.Flat · cited by 60RingHom.FlatAlgebraicGeometry.Flat · cited by 49AlgebraicGeometry.FlatAlgebraicGeometry.Etale · cited by 27AlgebraicGeometry.EtaleAlgebraicGeometry.LocallyOfFinitePresentation · cited by 26AlgebraicGeometry.Locally…Etale.iff_flat_and_formallyUn…CITED BYCITES

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