Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isAffine_of_isAffineHom
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.IsAffineHom f] [AlgebraicGeometry.IsAffine Y],
AlgebraicGeometry.IsAffine X- Cited by
- 9 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement and proof · cited by 32,603
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- AlgebraicGeometry.IsAffinestatement and proof · cited by 159
- AlgebraicGeometry.IsAffineHomstatement and proof · cited by 63
- AlgebraicGeometry.HasAffineProperty.iff_of_isAffineproof · cited by 21
Cited by9
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsIntegralHom.iff_universallyClosed_and_isAffineHomproof · cited by 2
- AlgebraicGeometry.Scheme.Hom.one_le_finrank_mapproof · cited by 1
- AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffineproof · cited by 1
- AlgebraicGeometry.Scheme.nonempty_of_isLimitproof · cited by 1
- AlgebraicGeometry.targetAffineLocally_affineAnd_iff_affineLocallyproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.one_le_finrank_iff_surjectiveproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.isIso_iff_finrank_eqproof · cited by 0
- AlgebraicGeometry.Scheme.Hom.isLocallyConstant_finrankproof · cited by 0
- AlgebraicGeometry.HasAffineProperty.descendsAlong_of_affineAndproof · cited by 0