Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsAffineOpen.fromSpec_preimage_basicOpen
∀ {X : AlgebraicGeometry.Scheme} {U : X.Opens} (hU : AlgebraicGeometry.IsAffineOpen U)
(f : ↑(X.presheaf.obj (Opposite.op U))),
(TopologicalSpace.Opens.map hU.fromSpec.base).obj (X.basicOpen f) = PrimeSpectrum.basicOpen f- Defined in
- Mathlib.AlgebraicGeometry.AffineScheme
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 151 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites28
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.objstatement and proof · cited by 19,642
- Oppositestatement · cited by 8,081
- CategoryTheory.Iso.invproof · cited by 6,514
- CategoryTheory.ConcreteCategory.homproof · cited by 4,022
- 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
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iffproof · cited by 2
- AlgebraicGeometry.IsAffineOpen.fromSpec_image_basicOpenproof · cited by 2
- AlgebraicGeometry.exists_smooth_of_formallySmooth_stalkproof · cited by 2
- AlgebraicGeometry.Scheme.IdealSheafData.opensRange_glueDataObjMapproof · cited by 1
- AlgebraicGeometry.IsAffineOpen.basicOpen_fromSpec_appproof · cited by 0