Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.Proj.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} (t : HomogeneousLocalization.NumDenSameDeg 𝒜 (Submonoid.powers f)),
  (TopologicalSpace.Opens.map (AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec 𝒜 f).base).obj
      (PrimeSpectrum.basicOpen (HomogeneousLocalization.mk t)) =
    (TopologicalSpace.Opens.comap { toFun := Subtype.val, continuous_toFun := ⋯ })
      (ProjectiveSpectrum.basicOpen 𝒜 ↑t.num)

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

0 results in Mathlib

Foundations

Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing