Theorems · Definition · algebraic geometry
AlgebraicGeometry.ProjectiveSpectrum.Proj.structureSheaf
{A : Type u_1} →
{σ : Type u_2} →
[inst : CommRing A] →
[inst_1 : SetLike σ A] →
[inst_2 : AddSubgroupClass σ A] →
(𝒜 : ℕ → σ) → [inst_3 : GradedRing 𝒜] → TopCat.Sheaf CommRingCat (ProjectiveSpectrum.top 𝒜)The structure sheaf on Proj 𝒜, valued in CommRing.
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- CommRingCatstatement · cited by 2,333
- SetLikestatement and proof · cited by 1,084
- GradedRingstatement and proof · cited by 424
- AddSubgroupClassstatement and proof · cited by 240
- TopCat.Sheafstatement · cited by 73
- ProjectiveSpectrum.topstatement · cited by 32
Cited by30
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Proj.stalkIso'statement and proof · cited by 7
- AlgebraicGeometry.sectionInBasicOpenstatement · cited by 6
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓproof · cited by 5
- AlgebraicGeometry.Proj.toSheafedSpaceproof · cited by 5
- AlgebraicGeometry.stalkToFiberRingHomstatement and proof · cited by 4
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSectionstatement · cited by 3
- AlgebraicGeometry.stalkToFiberRingHom_germstatement and proof · cited by 3
- AlgebraicGeometry.homogeneousLocalizationToStalkstatement and proof · cited by 2
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToΓ_ΓToStalkstatement and proof · cited by 2
- AlgebraicGeometry.Proj.stalkIso'_germstatement and proof · cited by 2
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_applystatement · cited by 1
- AlgebraicGeometry.ProjectiveSpectrum.Proj.awayToSection_germstatement · cited by 1