Theorems · Definition · algebraic geometry
RingHom.IsStandardSmoothOfRelativeDimension
ℕ → {R : Type u} → {S : Type v} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → PropA ring homomorphism R →+* S is standard smooth of relative dimension n if
S is standard smooth of relative dimension n as R-algebra.
- Cited by
- 18 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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
- RingHomstatement and proof · cited by 10,189
- Algebra.IsStandardSmoothOfRelativeDimensionproof · cited by 17
Cited by20
Results whose statement or proof uses this declaration.
- RingHom.IsStandardSmoothOfRelativeDimension.isStandardSmoothstatement and proof · cited by 3
- RingHom.IsStandardSmoothOfRelativeDimension.algebraMap_isLocalizationAwaystatement · cited by 3
- RingHom.isStandardSmoothOfRelativeDimension_isStableUnderBaseChangestatement and proof · cited by 2
- RingHom.isStandardSmoothOfRelativeDimension_respectsIsostatement and proof · cited by 2
- RingHom.IsStandardSmoothOfRelativeDimension.compstatement and proof · cited by 2
- RingHom.IsStandardSmoothOfRelativeDimension.equivstatement · cited by 2
- RingHom.etale_iff_isStandardSmoothOfRelativeDimension_zerostatement · cited by 1
- AlgebraicGeometry.Etale.eq_smoothOfRelativeDimension_zeroproof · cited by 1
- AlgebraicGeometry.SmoothOfRelativeDimension.casesOnstatement and proof · cited by 1
- AlgebraicGeometry.SmoothOfRelativeDimension.exists_isStandardSmoothOfRelativeDimensionstatement · cited by 1
- AlgebraicGeometry.SmoothOfRelativeDimension.smoothproof · cited by 1
- RingHom.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomialstatement and proof · cited by 1