Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.IdealSheafData.subschemeCover
{X : AlgebraicGeometry.Scheme} → (I : X.IdealSheafData) → I.subscheme.AffineOpenCoverThe subscheme associated to an ideal sheaf I is covered by Spec(Γ(X, U)/I(U)).
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 207 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Functor.objproof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- Set.Elemproof · cited by 7,166
- CategoryTheory.Iso.invproof · cited by 6,514
- TopCat.carrierproof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- HasQuotient.Quotientproof · cited by 2,301
- AlgebraicGeometry.PresheafedSpace.carrierproof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpaceproof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- AlgebraicGeometry.PresheafedSpace.presheafproof · cited by 1,104
Cited by13
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.inclusionproof · cited by 12
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeObjIsoproof · cited by 6
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeι_appproof · cited by 5
- AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusionstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.IdealSheafData.subschemeCover_map_subschemeιstatement · cited by 3
- AlgebraicGeometry.Scheme.IdealSheafData.inclusion_subschemeιproof · cited by 3
- AlgebraicGeometry.Scheme.Hom.toImageAuxproof · cited by 2
- AlgebraicGeometry.Scheme.IdealSheafData.subSchemeCover_map_inclusion_assocstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.toImageAux_specproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.inclusion_compproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.ker_subschemeι_appproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.inclusion_idproof · cited by 1