Theorems · Definition · commutative algebra

KaehlerDifferential.mapBaseChange

(R : Type u) →
  [inst : CommRing R] →
    (A : Type u_2) →
      (B : Type u_3) →
        [inst_1 : CommRing A] →
          [inst_2 : CommRing B] →
            [inst_3 : Algebra R A] →
              [inst_4 : Algebra A B] →
                [inst_5 : Algebra R B] → [IsScalarTower R A B] → TensorProduct A B Ω[A⁄R] →ₗ[B] Ω[B⁄R]

The lift of the map Ω[A⁄R] →ₗ[A] Ω[B⁄R] to the base change along A → B. This is the first map in the exact sequence B ⊗[A] Ω[A⁄R] → Ω[B⁄R] → Ω[B⁄A] → 0.

Defined in

Mathlib.RingTheory.Kaehler.Basic

Cited by

12 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingCommRingAlgebraAlgebraAlgebraIsScalarTower