Theorems · Theorem · algebraic geometry

AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eq_comap

∀ {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} (x : ↑((AlgebraicGeometry.Proj.toLocallyRingedSpace 𝒜).restrict ⋯).toTopCat),
  (CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec 𝒜 f).base) x =
    PrimeSpectrum.comap (HomogeneousLocalization.mapId 𝒜 ⋯)
      (IsLocalRing.closedPoint (HomogeneousLocalization.AtPrime 𝒜 (↑x).asHomogeneousIdeal.toIdeal))

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

1 results in Mathlib

Foundations

Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing