Theorems · Theorem · algebraic geometry

Algebra.IsStandardSmoothOfRelativeDimension.exists_etale_mvPolynomial

∀ (n : ℕ) (R : Type u) (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  [Algebra.IsStandardSmoothOfRelativeDimension n R S], ∃ g, g.Etale

Every standard smooth homomorphism R → S factors into R -> R[X₁,...,Xₙ] → S where n is the relative dimension and R[X₁,...,Xₙ] → S is etale.

Defined in

Mathlib.RingTheory.RingHom.StandardSmooth

Cited by

1 results in Mathlib

Foundations

Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraAlgebra.IsStandardSmoothOfRelativeDimension