Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.zeroLocus
(X : AlgebraicGeometry.Scheme) → {U : X.Opens} → Set ↑(X.presheaf.obj (Opposite.op U)) → Set ↥XThe zero locus of a set of sections s over an open set U is the closed set consisting of
the complement of U and of all points of U, where all elements of f vanish.
- Defined in
- Mathlib.AlgebraicGeometry.Scheme
- Cited by
- 60 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Oppositestatement · cited by 8,081
- 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 and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
Cited by69
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.extproof · cited by 16
- AlgebraicGeometry.Scheme.Hom.ker_applyproof · cited by 14
- AlgebraicGeometry.Scheme.IdealSheafData.supportSet_eq_iInter_zeroLocusstatement · cited by 6
- AlgebraicGeometry.Scheme.Hom.support_kerproof · cited by 6
- AlgebraicGeometry.Scheme.IdealSheafData.coe_support_interstatement · cited by 6
- AlgebraicGeometry.Scheme.IdealSheafData.ofIdealTopproof · cited by 4
- AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocusstatement and proof · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.gciproof · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdealproof · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.supportSet_interstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.codisjoint_zeroLocusstatement and proof · cited by 3
- AlgebraicGeometry.Scheme.IdealSheafData.mkOfMemSupportIffstatement and proof · cited by 2