Theorems · Definition · algebraic geometry
AlgebraicGeometry.Proj.toSpecZero
{σ : Type u_1} →
{A : Type u} →
[inst : CommRing A] →
[inst_1 : SetLike σ A] →
[inst_2 : AddSubgroupClass σ A] →
(𝒜 : ℕ → σ) →
[inst_3 : GradedRing 𝒜] → AlgebraicGeometry.Proj 𝒜 ⟶ AlgebraicGeometry.Spec (CommRingCat.of ↥(𝒜 0))The structure map Proj A ⟶ Spec A₀.
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 153 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Iso.invproof · cited by 6,514
- AlgebraicGeometry.Schemestatement · cited by 2,540
- SetLikestatement and proof · cited by 1,084
- AlgebraicGeometry.Specstatement · cited by 626
- GradedRingstatement and proof · cited by 424
- Submonoid.powersproof · cited by 408
- AlgebraicGeometry.Spec.mapproof · cited by 332
- CommRingCat.ofHomproof · cited by 259
- AddSubgroupClassstatement and proof · cited by 240
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.awayι_toSpecZerostatement · cited by 3
- AlgebraicGeometry.Proj.fromOfGlobalSections_toSpecZerostatement and proof · cited by 1
- AlgebraicGeometry.Proj.fromOfGlobalSections_toSpecZero_assocstatement and proof · cited by 0
- AlgebraicGeometry.Proj.awayι_toSpecZero_assocstatement and proof · cited by 0
- AlgebraicGeometry.Proj.valuativeCriterion_existencestatement and proof · cited by 0