Theorems · Definition · algebraic geometry

Module.Grassmannian.map

{R : Type u} →
  [inst : CommRing R] →
    {M : Type v} →
      [inst_1 : AddCommGroup M] →
        [inst_2 : Module R M] →
          {k : ℕ} →
            {A : Type w} →
              [inst_3 : CommRing A] →
                [inst_4 : Algebra R A] →
                  {B : Type w} →
                    [inst_5 : CommRing B] →
                      [inst_6 : Algebra R B] →
                        (A →ₐ[R] B) →
                          Module.Grassmannian A (TensorProduct R A M) k → Module.Grassmannian B (TensorProduct R B M) k

The map on Grassmannians induced by base change along an algebra map A → B. Given a submodule N of A ⊗[R] M, the image is the kernel of the composition B ⊗[R] M ≃ B ⊗[A] (A ⊗[R] M) → B ⊗[A] ((A ⊗[R] M) ⧸ N)`.

Defined in

Mathlib.RingTheory.Grassmannian

Cited by

4 results in Mathlib

Foundations

Depth 122 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleCommRingAlgebraCommRingAlgebra