Theorems · Theorem · algebraic geometry
Algebra.smoothLocus_eq_univ_iff
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.FinitePresentation R A], Algebra.smoothLocus R A = Set.univ ↔ Algebra.FormallySmooth R A- Defined in
- Mathlib.RingTheory.Smooth.Locus
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- SetLike.coeproof · cited by 8,199
- Set.univstatement and proof · cited by 3,945
- AlgEquivproof · cited by 1,681
- PrimeSpectrumstatement · cited by 625
- Submonoid.powersproof · cited by 408
- Localization.Awayproof · cited by 162
- Algebra.FormallySmoothstatement · cited by 60
- AlgEquiv.restrictScalarsproof · cited by 60
- Algebra.FinitePresentationstatement and proof · cited by 56
Cited by3
Results whose statement or proof uses this declaration.
- RingHom.Smooth.ofLocalizationSpanTargetproof · cited by 2
- Algebra.Smooth.of_formallySmooth_fiberproof · cited by 2
- Algebra.smoothLocus_eq_univproof · cited by 0