Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Proj.basicOpen_mono
∀ {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] (f g : A), f ∣ g → AlgebraicGeometry.Proj.basicOpen 𝒜 g ≤ AlgebraicGeometry.Proj.basicOpen 𝒜 f- Cited by
- 5 results in Mathlib
- Foundations
- Depth 152 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.carrierstatement · cited by 3,184
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement · cited by 1,149
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- inf_le_leftproof · cited by 286
- AddSubgroupClassstatement and proof · cited by 240
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.SpecMap_awayMap_awayιproof · cited by 5
- AlgebraicGeometry.Proj.awayMap_awayToSectionstatement and proof · cited by 2
- AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMapstatement and proof · cited by 1
- AlgebraicGeometry.Proj.basicOpenToSpec_SpecMap_awayMap_assocstatement and proof · cited by 1
- AlgebraicGeometry.Proj.awayMap_awayToSection_assocstatement and proof · cited by 0