Theorems · Definition · algebraic geometry
AlgebraicGeometry.StructureSheaf.globalSectionsIso
(R : Type u) → [inst : CommRing R] → CommRingCat.of R ≅ (AlgebraicGeometry.Spec.structureSheaf R).obj.obj (Opposite.op ⊤)
The ring isomorphism between the ring R and the global sections Γ(X, 𝒪ₓ).
- Defined in
- Mathlib.AlgebraicGeometry.StructureSheaf
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CommRingstatement and proof · cited by 17,173
- CategoryTheory.Functorstatement · cited by 16,252
- Top.topstatement and proof · cited by 9,680
- Oppositestatement · cited by 8,081
- Algebra.algebraMapproof · cited by 4,706
- CategoryTheory.Isostatement · cited by 3,963
- TopCat.carrierstatement · cited by 3,184
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- CategoryTheory.Presheaf.IsSheafstatement · cited by 991
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.StructureSheaf.globalSectionsIso_homstatement · cited by 0
- AlgebraicGeometry.StructureSheaf.globalSectionsIso_invstatement and proof · cited by 0