Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjCarrierIso
{X : AlgebraicGeometry.Scheme} →
(I : X.IdealSheafData) →
(U : ↑X.affineOpens) → ↑(I.glueDataObj U).toPresheafedSpace ≅ TopCat.of ↑(X.zeroLocus ↑(I.ideal U) ∩ ↑↑U)The underlying space of Spec (𝒪ₓ(U)/I(U)) is homeomorphic to its image in X.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 185 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites29
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- CategoryTheory.Functor.objstatement · cited by 19,642
- SetLike.coestatement · cited by 8,199
- Oppositestatement · cited by 8,081
- Set.Elemstatement and proof · cited by 7,166
- Idealstatement · cited by 4,748
- CategoryTheory.Isostatement · cited by 3,963
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.