Theorems · Definition · algebraic geometry

AlgebraicGeometry.ProjIsoSpecTopComponent.ToSpec.toFun

{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 ⋯).toPresheafedSpace →
                  ↑↑(AlgebraicGeometry.Spec.locallyRingedSpaceObj
                          (CommRingCat.of (HomogeneousLocalization.Away 𝒜 f))).toPresheafedSpace

The function between the basic open set D(f) in Proj to the corresponding basic open set in Spec A⁰_f. This is bundled into a continuous map in TopComponent.forward.

Defined in

Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme

Cited by

3 results in Mathlib

Foundations

Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingSetLikeAddSubgroupClassGradedRing