Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Proj.basicOpen_eq_iSup_proj
∀ {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 : A),
AlgebraicGeometry.Proj.basicOpen 𝒜 f = ⨆ i, AlgebraicGeometry.Proj.basicOpen 𝒜 ((GradedRing.proj 𝒜 i) f)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- AddMonoidHomstatement · cited by 3,230
- TopCat.carrierstatement · cited by 3,184
- iSupstatement · cited by 2,415
- 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
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