Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal
{X : AlgebraicGeometry.Scheme} → TopologicalSpace.Closeds ↥X → X.IdealSheafDataThe vanishing ideal sheaf of a closed set, which is the largest ideal sheaf whose support is equal to it. The reduced induced scheme structure on the closed set is the quotient of this ideal.
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 169 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.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Functor.objproof · cited by 19,642
- SetLike.coeproof · cited by 8,199
- Set.Elemproof · cited by 7,166
- Set.preimageproof · cited by 4,946
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
Cited by13
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.gcstatement · cited by 8
- AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdealstatement · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.map_vanishingIdealstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.coe_support_vanishingIdealstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_idealstatement and proof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_supportstatement · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_topstatement and proof · cited by 1
- AlgebraicGeometry.exists_mem_of_isClosed_of_nonemptyproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_antimonostatement · cited by 0
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_botstatement · cited by 0
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_iSupstatement · cited by 0
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_sSupstatement · cited by 0