Theorems · Definition · algebraic geometry

AlgebraicGeometry.ProjIsoSpecTopComponent.FromSpec.carrier.asHomogeneousIdeal

{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} →
                {m : ℕ} →
                  f ∈ 𝒜 m →
                    0 < m →
                      ↑↑(AlgebraicGeometry.Spec.locallyRingedSpaceObj
                                (CommRingCat.of (HomogeneousLocalization.Away 𝒜 f))).toPresheafedSpace →
                        HomogeneousIdeal 𝒜

For a prime ideal q in A⁰_f, the set {a | aᵢᵐ/fⁱ ∈ q} as a homogeneous ideal.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

1 results in Mathlib

Foundations

Depth 125 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing