Theorems · Theorem · algebraic geometry
Algebra.IsSmoothAt.exists_notMem_smooth
∀ (R : Type u_1) {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.FinitePresentation R A] (p : Ideal A) [inst_4 : p.IsPrime] [Algebra.IsSmoothAt R p],
∃ f ∉ p, Algebra.Smooth R (Localization.Away f)- Defined in
- Mathlib.RingTheory.Smooth.Locus
- Cited by
- 2 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.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · 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.imageproof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Set.rangeproof · cited by 4,705
- TopologicalSpace.Opensproof · cited by 2,040
- Ideal.IsPrimestatement and proof · cited by 827
- PrimeSpectrumproof · cited by 625
- Submonoid.powersstatement · cited by 408
- PrimeSpectrum.zeroLocusproof · cited by 164
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.IsSmoothAt.exists_notMem_isStandardSmoothproof · cited by 2
- AlgebraicGeometry.exists_smooth_of_formallySmooth_stalkproof · cited by 2