Theorems · Theorem · algebraic geometry
ProjectiveSpectrum.basicOpen_eq_union_of_projection
∀ {A : Type u_1} {σ : Type u_2} [inst : CommRing A] [inst_1 : SetLike σ A] [inst_2 : AddSubmonoidClass σ A] (𝒜 : ℕ → σ)
[inst_3 : GradedRing 𝒜] (f : A),
ProjectiveSpectrum.basicOpen 𝒜 f = ⨆ i, ProjectiveSpectrum.basicOpen 𝒜 ((GradedRing.proj 𝒜 i) f)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- SetLike.coeproof · cited by 8,199
- Set.rangeproof · cited by 4,705
- AddMonoidHomstatement · cited by 3,230
- iSupstatement and proof · cited by 2,415
- Set.extproof · cited by 2,266
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- AddSubmonoidClassstatement and proof · cited by 346
- SetLike.mem_coeproof · cited by 302
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.basicOpen_eq_iSup_projproof · cited by 0