Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.pointSmallEtaleFiberObjToPreimage_surjective
∀ {S : AlgebraicGeometry.Scheme} {Ω : Type u} [inst : Field Ω] [inst_1 : IsSepClosed Ω]
(s : AlgebraicGeometry.Spec (CommRingCat.of Ω) ⟶ S) {s₀ : ↥S} (hs₀ : s default = s₀) (X : S.Etale),
Function.Surjective (AlgebraicGeometry.Scheme.pointSmallEtaleFiberObjToPreimage s hs₀)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 208 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsSepClosed
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites56
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Quiver.Homstatement and proof · cited by 32,603
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- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Top.topstatement · cited by 9,680
- Fieldstatement and proof · cited by 7,404
- Set.Elemstatement and proof · cited by 7,166
- CategoryTheory.Category.assocproof · cited by 6,433
- Set.preimagestatement and proof · cited by 4,946
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- Equiv.symmproof · cited by 3,681
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.isConservative_pointSmallEtaleproof · cited by 1