Theorems · Definition · algebraic geometry

AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.carrier

{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} →
                ↑((AlgebraicGeometry.Proj.toLocallyRingedSpace 𝒜).restrict ⋯).toTopCat →
                  Ideal (HomogeneousLocalization.Away 𝒜 f)

For any x in Proj| (pbo f), the corresponding ideal in Spec A⁰_f. This fact that this ideal is prime is proven in TopComponent.Forward.toFun.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

5 results in Mathlib

Foundations

Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing