Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.irreducibleComponentsEquiv
{X S : AlgebraicGeometry.Scheme} →
(f : X ⟶ S) →
[AlgebraicGeometry.GeometricallyIrreducible f] →
IsOpenMap ⇑f → ↑(irreducibleComponents ↥X) ≃ ↑(irreducibleComponents ↥S)If f : X ⟶ S is geometrically irreducible and open,
then f induces an equivalence between the irreducible components of X and S.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites25
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
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.irreducibleComponentsEquiv_apply_coestatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Hom.irreducibleComponentsEquiv_symm_apply_coestatement and proof · cited by 0