Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isReduced_of_isOpenImmersion
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.IsOpenImmersion f] [AlgebraicGeometry.IsReduced Y],
AlgebraicGeometry.IsReduced X- Defined in
- Mathlib.AlgebraicGeometry.Properties
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- CategoryTheory.Functor.objproof · cited by 19,642
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- AlgebraicGeometry.Scheme.Opensproof · cited by 1,149
- AlgebraicGeometry.PresheafedSpace.presheafproof · cited by 1,104
- CommRingCat.carrierproof · cited by 1,096
- CategoryTheory.Iso.symmproof · cited by 993
- AlgebraicGeometry.IsOpenImmersionstatement and proof · cited by 476
- CategoryTheory.invproof · cited by 467
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.isField_stalk_of_closure_mem_irreducibleComponentsproof · cited by 1
- AlgebraicGeometry.eq_zero_of_basicOpen_eq_botproof · cited by 1
- AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpaceproof · cited by 1
- AlgebraicGeometry.isReduced_of_isAffine_isReducedproof · cited by 0