Theorems · Theorem · commutative algebra

tensorKaehlerQuotKerSqEquiv_symm_tmul_D

∀ {R : Type u_1} {P : Type u_2} {S : Type u_3} [inst : CommRing R] [inst_1 : CommRing P] [inst_2 : CommRing S]
  [inst_3 : Algebra R P] [inst_4 : Algebra P S] [inst_5 : Algebra R S] [inst_6 : IsScalarTower R P S] (s : S) (t : P),
  (tensorKaehlerQuotKerSqEquiv R P S).symm (s ⊗ₜ[P] (KaehlerDifferential.D R P) t) =
    s ⊗ₜ[P ⧸ RingHom.ker (algebraMap P S) ^ 2]
      (KaehlerDifferential.D R (P ⧸ RingHom.ker (algebraMap P S) ^ 2))
        ((Ideal.Quotient.mk (RingHom.ker (algebraMap P S) ^ 2)) t)

Defined in

Mathlib.RingTheory.Smooth.Kaehler

Cited by

1 results in Mathlib

Foundations

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

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraIsScalarTower