Theorems · Theorem · algebraic geometry
AlgebraicGeometry.exists_isFinite_morphismRestrict_of_finite_preimage_singleton
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.IsProper f] (y : ↥Y),
(⇑f ⁻¹' {y}).Finite → ∃ V, y ∈ V ∧ AlgebraicGeometry.IsFinite (f ∣_ V)[Stacks Tag 02UP](https://stacks.math.columbia.edu/tag/02UP)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 239 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.IsProper
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites51
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.preimagestatement and proof · cited by 4,946
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- Finiteproof · cited by 3,029
- Compl.complproof · cited by 2,925
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
Cited by1
Results whose statement or proof uses this declaration.