Theorems · Definition · algebraic geometry
AlgebraicGeometry.Proj
{A : Type u_1} →
{σ : Type u_2} →
[inst : CommRing A] →
[inst_1 : SetLike σ A] → [inst_2 : AddSubgroupClass σ A] → (𝒜 : ℕ → σ) → [GradedRing 𝒜] → AlgebraicGeometry.SchemeThis is the scheme Proj(A) for any ℕ-graded ring A.
- Cited by
- 63 results in Mathlib
- Foundations
- Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement · cited by 2,540
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- AddSubgroupClassstatement and proof · cited by 240
- AlgebraicGeometry.LocallyRingedSpaceproof · cited by 205
- AlgebraicGeometry.Proj.toLocallyRingedSpaceproof · cited by 26
Cited by78
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.basicOpenstatement · cited by 38
- AlgebraicGeometry.Proj.awayιstatement · cited by 30
- AlgebraicGeometry.Proj.pullbackAwayιIsostatement · cited by 12
- AlgebraicGeometry.Proj.basicOpenIsoSpecstatement · cited by 11
- AlgebraicGeometry.Proj.awayToSectionstatement · cited by 9
- AlgebraicGeometry.Proj.mapstatement · cited by 9
- AlgebraicGeometry.Proj.toBasicOpenOfGlobalSectionsstatement · cited by 7
- AlgebraicGeometry.Proj.fromOfGlobalSectionsstatement · cited by 6
- AlgebraicGeometry.Proj.SpecMap_awayMap_awayιstatement and proof · cited by 5
- AlgebraicGeometry.Proj.basicOpenToSpecstatement · cited by 5
- AlgebraicGeometry.Proj.basicOpen_monostatement · cited by 5
- AlgebraicGeometry.Proj.toSpecZerostatement and proof · cited by 5