Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Proj.fromOfGlobalSections_preimage_basicOpen

∀ {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},
  0 < n →
    r ∈ 𝒜 n →
      (TopologicalSpace.Opens.map (AlgebraicGeometry.Proj.fromOfGlobalSections 𝒜 f hf).base).obj
          (AlgebraicGeometry.Proj.basicOpen 𝒜 r) =
        X.basicOpen (f r)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic

Cited by

2 results in Mathlib

Foundations

Depth 164 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing