Theorems · Inductive type · commutative algebra
Algebra.IsStandardSmooth
(R : Type u) → (S : Type v) → [inst : CommRing R] → [inst_1 : CommRing S] → [Algebra R S] → Prop
An R-algebra S is called standard smooth, if there
exists a submersive presentation.
- Defined in
- Mathlib.RingTheory.Smooth.StandardSmooth
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by21
Results whose statement or proof uses this declaration.
- RingHom.IsStandardSmoothproof · cited by 16
- Algebra.IsStandardSmooth.casesOnstatement and proof · cited by 4
- Algebra.IsSmoothAt.exists_notMem_isStandardSmoothstatement and proof · cited by 2
- Algebra.SubmersivePresentation.isStandardSmoothstatement · cited by 2
- Algebra.Etale.iff_isStandardSmoothOfRelativeDimension_zeroproof · cited by 2
- Algebra.IsStandardSmooth.of_basis_kaehlerDifferentialstatement · cited by 2
- Algebra.IsStandardSmooth.outstatement and proof · cited by 1
- Algebra.IsStandardSmooth.transstatement and proof · cited by 1
- Algebra.IsStandardSmoothOfRelativeDimension.isStandardSmoothstatement · cited by 1
- Algebra.IsStandardSmooth.of_algEquivstatement and proof · cited by 1
- Algebra.IsSmoothAt.exists_isStandardEtale_mvPolynomialproof · cited by 1
- RingHom.Smooth.locally_isStandardSmoothproof · cited by 1