Theorems · Definition · algebraic geometry

Module.Grassmannian.baseChangeMkQEquiv

{R : Type u} →
  [inst : CommRing R] →
    {M : Type v} →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module R M] →
          {A : Type w} →
            [inst_3 : CommRing A] →
              [inst_4 : Algebra R A] →
                {B : Type w} →
                  [inst_5 : CommRing B] →
                    [inst_6 : Algebra R B] →
                      [inst_7 : Algebra A B] →
                        [inst_8 : IsScalarTower R A B] →
                          (N : Submodule A (TensorProduct R A M)) →
                            (TensorProduct R B M ⧸ (Module.Grassmannian.baseChangeMkQ B N).ker) ≃ₗ[B]
                              TensorProduct A B (TensorProduct R A M ⧸ N)

The B-linear equivalence (B ⊗[R] M) ⧸ ker (baseChangeMkQ N) ≃ₗ[B] B ⊗[A] ((A ⊗[R] M) ⧸ N) underlying Module.Grassmannian.map.

Defined in

Mathlib.RingTheory.Grassmannian

Cited by

0 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower