Theorems · Theorem · commutative algebra

Algebra.Extension.tensorCotangentInvFun_smul_mk

∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
  [inst_3 : Algebra R S] [inst_4 : Algebra R T] [inst_5 : Algebra S T] {P : Algebra.Extension R S}
  {Q : Algebra.Extension R T} (f : P.Hom Q) [alg : Algebra P.Ring Q.Ring]
  (halg : algebraMap P.Ring Q.Ring = f.toRingHom)
  (H : Function.Bijective ⇑(LinearMap.liftBaseChange Q.Ring (f.mapKer halg))) (x : Q.Ring) (y : ↥P.ker),
  (Algebra.Extension.tensorCotangentInvFun f halg H) (x • Algebra.Extension.Cotangent.mk ⟨f.toRingHom ↑y, ⋯⟩) =
    x • 1 ⊗ₜ[S] Algebra.Extension.Cotangent.mk y

Defined in

Mathlib.RingTheory.Etale.Kaehler

Cited by

0 results in Mathlib

Foundations

Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraAlgebra