Theorems · Definition · algebraic geometry
Algebra.smoothLocus
(R : Type u_1) → (A : Type u_2) → [inst : CommRing R] → [inst_1 : CommRing A] → [Algebra R A] → Set (PrimeSpectrum A)
Algebra.smoothLocus R A is the set of primes p of A
such that Aₚ is formally smooth over R.
- Defined in
- Mathlib.RingTheory.Smooth.Locus
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 46 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Set.ofPredproof · cited by 6,101
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealproof · cited by 333
- Algebra.IsSmoothAtproof · cited by 6
Cited by11
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.formallySmooth_stalkMap_iffstatement · cited by 3
- Algebra.basicOpen_subset_smoothLocus_iffstatement · cited by 3
- Algebra.smoothLocus_eq_univ_iffstatement and proof · cited by 3
- Algebra.IsSmoothAt.exists_notMem_smoothproof · cited by 2
- Algebra.smoothLocus_eq_compl_support_interstatement and proof · cited by 2
- RingHom.Smooth.ofLocalizationSpanTargetproof · cited by 2
- Algebra.isOpen_smoothLocusstatement and proof · cited by 2
- Algebra.etaleLocus_eq_unramfiedLocus_inter_smoothLocusstatement · cited by 1
- Algebra.smoothLocus_comap_of_isLocalizationstatement · cited by 1
- Algebra.smoothLocus_eq_univstatement · cited by 0
- Algebra.basicOpen_subset_smoothLocus_iff_smoothstatement · cited by 0