Mathlib Map

Theorems · Definition · algebraic geometry

RingHom.IsStandardSmoothOfRelativeDimension

ℕ → {R : Type u} → {S : Type v} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop

A ring homomorphism R →+* S is standard smooth of relative dimension n if S is standard smooth of relative dimension n as R-algebra.

Defined in
Mathlib.RingTheory.RingHom.StandardSmooth
Cited by
18 results in Mathlib
Foundations
Depth 19 from the axioms · uses no axioms
Assumes
CommRingCommRing

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

RingHom.IsStandardSmoothOfRelativeDimension.isStandardSmooth · cited by 3IsStandardSmoothOfRelativ…RingHom.IsStandardSmoothOfRelativeDimension.algebraMap_isLocalizationAway · cited by 3IsStandardSmoothOfRelativ…RingHom.isStandardSmoothOfRelativeDimension_isStableUnderBaseChange · cited by 2RingHom.isStandardSmoothO…RingHom.isStandardSmoothOfRelativeDimension_respectsIso · cited by 2RingHom.isStandardSmoothO…RingHom.IsStandardSmoothOfRelativeDimension.comp · cited by 2IsStandardSmoothOfRelativ…RingHom.IsStandardSmoothOfRelativeDimension.equiv · cited by 2IsStandardSmoothOfRelativ…RingHom.etale_iff_isStandardSmoothOfRelativeDimension_zero · cited by 1RingHom.etale_iff_isStand…AlgebraicGeometry.Etale.eq_smoothOfRelativeDimension_zero · cited by 1Etale.eq_smoothOfRelative…AlgebraicGeometry.SmoothOfRelativeDimension.casesOn · cited by 1SmoothOfRelativeDimension…AlgebraicGeometry.SmoothOfRelativeDimension.exists_isStandardSmoothOfRelativeDimension · cited by 1SmoothOfRelativeDimension…AlgebraicGeometry.SmoothOfRelativeDimension.smooth · cited by 1SmoothOfRelativeDimension…RingHom.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial · cited by 1IsStandardSmoothOfRelativ…RingHom.IsStandardSmoothOfRelativeDimension.toAlgebra · cited by 0IsStandardSmoothOfRelativ…AlgebraicGeometry.SmoothOfRelativeDimension.recOn · cited by 0SmoothOfRelativeDimension…RingHom.isStandardSmoothOfRelativeDimension_algebraMap · cited by 0RingHom.isStandardSmoothO…CommRing · cited by 17173CommRingRingHom · cited by 10189RingHomAlgebra.IsStandardSmoothOfRelativeDimension · cited by 17Algebra.IsStandardSmoothO…RingHom.IsStandardSmoothOfRel…CITED BYCITES

Cites3

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by20

Results whose statement or proof uses this declaration.