Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.isoSpec_inv_preimage_zeroLocus
∀ (X : AlgebraicGeometry.Scheme) [inst : AlgebraicGeometry.IsAffine X] (s : Set ↑(X.presheaf.obj (Opposite.op ⊤))), ⇑X.isoSpec.inv ⁻¹' X.zeroLocus s = PrimeSpectrum.zeroLocus s
- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.IsAffine
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites37
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- Top.topstatement and proof · cited by 9,680
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.invstatement and proof · cited by 6,514
- CategoryTheory.CategoryStruct.idproof · cited by 6,235
- Set.preimagestatement and proof · cited by 4,946
- 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
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.isoSpec_inv_image_zeroLocusproof · cited by 0