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Theorems · Definition · algebraic geometry

AlgebraicGeometry.Scheme.IdealSheafData.ideal

{X : AlgebraicGeometry.Scheme} → X.IdealSheafData → (U : ↑X.affineOpens) → Ideal ↑(X.presheaf.obj (Opposite.op ↑U))

The component of an ideal sheaf at an affine open.

Defined in
Mathlib.AlgebraicGeometry.IdealSheaf.Basic
Cited by
88 results in Mathlib
Foundations
Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.IdealSheafData.glueDataObj · cited by 24IdealSheafData.glueDataObjAlgebraicGeometry.Scheme.IdealSheafData.glueDataObjι · cited by 20IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.IdealSheafData.ext · cited by 16IdealSheafData.extAlgebraicGeometry.Scheme.Hom.ker_apply · cited by 14Hom.ker_applyAlgebraicGeometry.Scheme.IdealSheafData.radical · cited by 10IdealSheafData.radicalAlgebraicGeometry.Scheme.IdealSheafData.subschemeCover · cited by 10IdealSheafData.subschemeC…AlgebraicGeometry.Scheme.IdealSheafData.ker_subschemeι · cited by 7IdealSheafData.ker_subsch…AlgebraicGeometry.Scheme.Hom.support_ker · cited by 6Hom.support_kerAlgebraicGeometry.Scheme.IdealSheafData.coe_support_inter · cited by 6IdealSheafData.coe_suppor…AlgebraicGeometry.Scheme.IdealSheafData.subschemeObjIso · cited by 6IdealSheafData.subschemeO…AlgebraicGeometry.Scheme.IdealSheafData.supportSet_eq_iInter_zeroLocus · cited by 6IdealSheafData.supportSet…AlgebraicGeometry.Scheme.IdealSheafData.glueDataObjMap · cited by 5IdealSheafData.glueDataOb…AlgebraicGeometry.Scheme.IdealSheafData.map_ideal · cited by 5IdealSheafData.map_idealAlgebraicGeometry.Scheme.IdealSheafData.subschemeι_app · cited by 5IdealSheafData.subschemeι…AlgebraicGeometry.Scheme.Hom.range_subset_ker_support · cited by 4Hom.range_subset_ker_supp…Set · cited by 53352SetCategoryTheory.Functor.obj · cited by 19642Functor.objOpposite · cited by 8081OppositeSet.Elem · cited by 7166Set.ElemIdeal · cited by 4748IdealTopCat.carrier · cited by 3184TopCat.carrierAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCommRingCat · cited by 2333CommRingCatTopologicalSpace.Opens · cited by 2040TopologicalSpace.OpensAlgebraicGeometry.PresheafedSpace.carrier · cited by 2020PresheafedSpace.carrierAlgebraicGeometry.SheafedSpace.toPresheafedSpace · cited by 1988SheafedSpace.toPresheafed…AlgebraicGeometry.LocallyRingedSpace.toSheafedSpace · cited by 1892LocallyRingedSpace.toShea…AlgebraicGeometry.Scheme.toLocallyRingedSpace · cited by 1734Scheme.toLocallyRingedSpa…AlgebraicGeometry.Scheme.Opens · cited by 1149Scheme.OpensAlgebraicGeometry.PresheafedSpace.presheaf · cited by 1104PresheafedSpace.presheafIdealSheafData.idealCITED BYCITES

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Cited by101

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