Theorems · Theorem · algebraic geometry
Algebra.smoothLocus_eq_compl_support_inter
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
[Algebra.EssFiniteType R A],
Algebra.smoothLocus R A = (Module.support A (Algebra.H1Cotangent R A))ᶜ ∩ Module.freeLocus A Ω[A⁄R]- Defined in
- Mathlib.RingTheory.Smooth.Locus
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- LinearEquivproof · cited by 3,317
- Compl.complstatement and proof · cited by 2,925
- Set.extproof · cited by 2,266
- LinearEquiv.symmproof · cited by 1,461
- PrimeSpectrumstatement and proof · cited by 625
- Module.Freeproof · cited by 597
- Ideal.primeComplproof · cited by 462
- PrimeSpectrum.asIdealproof · cited by 333
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.basicOpen_subset_smoothLocus_iffproof · cited by 3
- Algebra.isOpen_smoothLocusproof · cited by 2