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Theorems · Inductive type · algebraic geometry

AlgebraicGeometry.Etale

{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → Prop

A morphism of schemes f : X ⟶ Y is étale if for each affine U ⊆ Y and V ⊆ f ⁻¹' U, The induced map Γ(Y, U) ⟶ Γ(X, V) is étale.

Defined in
Mathlib.AlgebraicGeometry.Morphisms.Etale
Cited by
27 results in Mathlib
Foundations
Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
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AlgebraicGeometry.Scheme.Etale · cited by 16Scheme.EtaleAlgebraicGeometry.Scheme.smallEtaleTopology · cited by 9Scheme.smallEtaleTopologyAlgebraicGeometry.Scheme.Etale.forget · cited by 6Etale.forgetAlgebraicGeometry.Scheme.AffineEtale.Spec · cited by 4AffineEtale.SpecAlgebraicGeometry.Scheme.pointSmallEtaleFiberObjToPreimage · cited by 4Scheme.pointSmallEtaleFib…AlgebraicGeometry.Scheme.AffineEtale · cited by 4Scheme.AffineEtaleAlgebraicGeometry.Scheme.AffineEtale.mk · cited by 3AffineEtale.mkAlgebraicGeometry.Scheme.etaleTopology · cited by 2Scheme.etaleTopologyAlgebraicGeometry.Scheme.Etale.mk · cited by 2Etale.mkAlgebraicGeometry.etale_iff · cited by 1AlgebraicGeometry.etale_i…AlgebraicGeometry.Scheme.Hom.exists_mem_and_isIso_morphismRestrict_toNormalization · cited by 1Hom.exists_mem_and_isIso_…AlgebraicGeometry.Etale.casesOn · cited by 1Etale.casesOnAlgebraicGeometry.Etale.eq_smoothOfRelativeDimension_zero · cited by 1Etale.eq_smoothOfRelative…AlgebraicGeometry.Etale.etale_appLE · cited by 1Etale.etale_appLEAlgebraicGeometry.Etale.iff_flat_and_formallyUnramified · cited by 1Etale.iff_flat_and_formal…Quiver.Hom · cited by 32603Quiver.HomAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeAlgebraicGeometry.EtaleCITED BYCITES

Cites2

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Cited by44

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