Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.ker_apply
∀ {X Y : AlgebraicGeometry.Scheme} (f : X.Hom Y) [AlgebraicGeometry.QuasiCompact f] (U : ↑Y.affineOpens),
f.ker.ideal U = RingHom.ker (CommRingCat.Hom.hom (f.app ↑U))- Cited by
- 14 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites69
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- RingHomstatement · cited by 10,189
- CategoryTheory.Functor.mapproof · cited by 8,698
- SetLike.coeproof · cited by 8,199
- Oppositestatement · cited by 8,081
- Set.Elemstatement and proof · cited by 7,166
- Idealstatement · cited by 4,748
- Algebra.algebraMapproof · cited by 4,706
Cited by14
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.IdealSheafData.ker_subschemeιproof · cited by 7
- AlgebraicGeometry.Scheme.Hom.iInf_ker_openCover_map_comp_applyproof · cited by 2
- AlgebraicGeometry.Scheme.ker_ideal_of_isPullback_of_isOpenImmersionproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.ker_eq_bot_of_isIsoproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.app_injectiveproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.toImage_app_injectiveproof · cited by 1
- AlgebraicGeometry.Scheme.IdealSheafData.ideal_mapproof · cited by 1
- AlgebraicGeometry.IsClosedImmersion.isIso_of_injective_of_isAffineproof · cited by 0
- AlgebraicGeometry.Scheme.ker_morphismRestrict_idealproof · cited by 0
- AlgebraicGeometry.Scheme.ker_toSpecΓproof · cited by 0
- AlgebraicGeometry.isDominant_of_of_appTop_injectiveproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.ker_toNormalizationproof · cited by 0