Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.IdealSheafData.supportSet_eq_iInter_zeroLocus
∀ {X : AlgebraicGeometry.Scheme} (self : X.IdealSheafData), self.supportSet = ⋂ U, X.zeroLocus ↑(self.ideal U)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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 · cited by 7,166
- Idealstatement · cited by 4,748
- 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
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
Cited by6
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iff_of_memproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.supportSet_subset_zeroLocusproof · cited by 0
- AlgebraicGeometry.Scheme.IdealSheafData.mem_supportSet_iffproof · cited by 0
- AlgebraicGeometry.Scheme.IdealSheafData.mem_support_iffproof · cited by 0