Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.fromSpec_image_zeroLocus
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} (hU : AlgebraicGeometry.IsAffineOpen U)
(s : Set ↑(X.presheaf.obj (Opposite.op U))), ⇑hU.fromSpec '' PrimeSpectrum.zeroLocus s = X.zeroLocus s ∩ ↑U- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 154 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- SetLike.coestatement and proof · cited by 8,199
- Oppositestatement · cited by 8,081
- Set.imagestatement and proof · cited by 5,609
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- ContinuousMapstatement · cited by 2,491
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.le_support_iff_le_vanishingIdealproof · cited by 4
- AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjι_ιproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.vanishingIdeal_supportproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.support_eq_bot_iffproof · cited by 0