Theorems · Theorem · commutative algebra
Algebra.IsStandardSmoothOfRelativeDimension.out
∀ {n : ℕ} {R : Type u} {S : Type v} {inst : CommRing R} {inst_1 : CommRing S} {inst_2 : Algebra R S}
[self : Algebra.IsStandardSmoothOfRelativeDimension n R S],
∃ ι σ, ∃ (x : Finite σ) (_ : Finite ι), ∃ P, P.dimension = n- Defined in
- Mathlib.RingTheory.Smooth.StandardSmooth
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Finitestatement · cited by 3,029
- Algebra.PreSubmersivePresentation.toPresentationstatement · cited by 84
- Algebra.SubmersivePresentationstatement · cited by 52
- Algebra.SubmersivePresentation.toPreSubmersivePresentationstatement · cited by 47
- Algebra.IsStandardSmoothOfRelativeDimensionstatement and proof · cited by 17
- Algebra.Presentation.dimensionstatement · cited by 16
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomialproof · cited by 1
- Algebra.IsStandardSmoothOfRelativeDimension.exists_subalgebra_fgproof · cited by 1
- Algebra.IsStandardSmoothOfRelativeDimension.isStandardSmoothproof · cited by 1