Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.isOpen_smoothLocus
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.LocallyOfFinitePresentation f],
IsOpen {x | (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.stalkMap f x)).FormallySmooth}- Cited by
- 0 results in Mathlib
- Foundations
- Depth 159 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites40
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- Set.ofPredstatement and proof · cited by 6,101
- CategoryTheory.ConcreteCategory.homstatement · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- IsOpenstatement · cited by 2,400
- CommRingCatstatement · cited by 2,333
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.smoothLocusproof · cited by 6