Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec_preimage_basicOpen

∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubgroupClass σ A] {𝒜 : ℕ → σ}
  [inst_3 : GradedRing 𝒜] {f : A} (z : HomogeneousLocalization.NumDenSameDeg 𝒜 (Submonoid.powers f)),
  ⇑(CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.ProjIsoSpecTopComponent.toSpec 𝒜 f)) ⁻¹'
      ↑(PrimeSpectrum.basicOpen (HomogeneousLocalization.mk z)) =
    Subtype.val ⁻¹' ↑(ProjectiveSpectrum.basicOpen 𝒜 ↑z.num)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

1 results in Mathlib

Foundations

Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing