Theorems · Theorem · algebraic geometry
Algebra.isOpen_smoothLocus
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.FinitePresentation R A], IsOpen (Algebra.smoothLocus R A)- Defined in
- Mathlib.RingTheory.Smooth.Locus
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 137 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites45
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Set.preimageproof · cited by 4,946
- Algebra.algebraMapproof · cited by 4,706
- Set.rangeproof · cited by 4,705
- LinearEquivproof · cited by 3,317
- Compl.complproof · cited by 2,925
- IsOpenstatement and proof · cited by 2,400
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.IsSmoothAt.exists_notMem_smoothproof · cited by 2
- Algebra.isOpen_etaleLocusproof · cited by 1