Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.smoothLocus
{X Y : AlgebraicGeometry.Scheme} → (f : X ⟶ Y) → [AlgebraicGeometry.LocallyOfFinitePresentation f] → X.OpensThe set of points smooth over a base, as a Scheme.Opens.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Set.ofPredproof · cited by 6,101
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
- CommRingCat.Hom.homproof · cited by 432
- AlgebraicGeometry.Scheme.Hom.stalkMapproof · cited by 82
- AlgebraicGeometry.LocallyOfFinitePresentationstatement and proof · cited by 26
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.mem_smoothLocusstatement · cited by 2
- AlgebraicGeometry.Scheme.Hom.genericPoint_mem_smoothLocus_of_perfectFieldstatement · cited by 1
- AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_topstatement · cited by 1
- AlgebraicGeometry.Scheme.Hom.preimage_smoothLocus_eqstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.Hom.smoothLocus_eq_top_iffstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Hom.dense_smoothLocus_of_perfectFieldstatement and proof · cited by 0