Theorems · Theorem · field theory

Algebra.FormallyEtale.equivPiOfIsSepClosed_comap

∀ {K : Type u_1} {A : Type u} [inst : Field K] [inst_1 : CommRing A] [inst_2 : Algebra K A] {B : Type u_3}
  [inst_3 : CommRing B] [inst_4 : Algebra.EssFiniteType K A] [inst_5 : Algebra.FormallyEtale K A] [inst_6 : Algebra K B]
  [inst_7 : Algebra.EssFiniteType K B] [inst_8 : Algebra.FormallyEtale K B] [inst_9 : IsSepClosed K] (f : A →ₐ[K] B)
  (x : A) (p : PrimeSpectrum B),
  (Algebra.FormallyEtale.equivPiOfIsSepClosed K A) x (PrimeSpectrum.comap (↑f) p) =
    (Algebra.FormallyEtale.equivPiOfIsSepClosed K B) (f x) p

Defined in

Mathlib.RingTheory.Etale.Field

Cited by

0 results in Mathlib

Foundations

Depth 201 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldCommRingAlgebraCommRingAlgebra.EssFiniteTypeAlgebra.FormallyEtaleAlgebraAlgebra.EssFiniteTypeAlgebra.FormallyEtaleIsSepClosed