Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsZariskiLocalAtSource.of_isOpenImmersion
∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsZariskiLocalAtSource P]
{X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [P.ContainsIdentities] [AlgebraicGeometry.IsOpenImmersion f], P f- Cited by
- 5 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Category.comp_idproof · cited by 2,119
- AlgebraicGeometry.IsOpenImmersionstatement and proof · cited by 476
- CategoryTheory.MorphismProperty.ContainsIdentitiesstatement and proof · cited by 94
- AlgebraicGeometry.IsZariskiLocalAtSourcestatement and proof · cited by 37
- CategoryTheory.MorphismProperty.id_memproof · cited by 23
- AlgebraicGeometry.IsZariskiLocalAtSource.compproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsLocalIso.le_of_isZariskiLocalAtSourceproof · cited by 2
- AlgebraicGeometry.Scheme.exists_hom_isAffine_of_isZariskiLocalAtSourceproof · cited by 1
- AlgebraicGeometry.Scheme.zariskiPrecoverage_le_propQCPrecoverageproof · cited by 1
- AlgebraicGeometry.IsZariskiLocalAtSource.isZariskiLocalAtTargetproof · cited by 0
- AlgebraicGeometry.HasRingHomProperty.of_isOpenImmersionproof · cited by 0