Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsFinite.finite_preimage_singleton
Deprecated since 2026-02-05Use AlgebraicGeometry.Scheme.Hom.finite_preimage_singleton instead.
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.LocallyQuasiFinite f]
[AlgebraicGeometry.QuasiCompact f] (y : ↥Y), (⇑f ⁻¹' {y}).FiniteAlias of AlgebraicGeometry.Scheme.Hom.finite_preimage_singleton.
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- Foundations
- Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homstatement · cited by 32,603
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- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
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- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
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