Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Proj.fromOfGlobalSections_morphismRestrict

∀ {σ : Type u_1} {A : Type u} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] (𝒜 : ℕ → σ)
  [inst_3 : GradedRing 𝒜] {X : AlgebraicGeometry.Scheme} (f : A →+* ↑(X.presheaf.obj (Opposite.op ⊤)))
  (hf : Ideal.map f (HomogeneousIdeal.irrelevant 𝒜).toIdeal = ⊤) {r : A} {n : ℕ} (hn : 0 < n) (hr : r ∈ 𝒜 n),
  AlgebraicGeometry.Proj.fromOfGlobalSections 𝒜 f hf ∣_ AlgebraicGeometry.Proj.basicOpen 𝒜 r =
    CategoryTheory.CategoryStruct.comp (X.isoOfEq ⋯).hom
      (AlgebraicGeometry.Proj.toBasicOpenOfGlobalSections 𝒜 f ⋯ hn hr)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic

Cited by

1 results in Mathlib

Foundations

Depth 165 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing