Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.PartialMap.isDominant_hom_iff_isDominant_restrict_hom
∀ {X Y : AlgebraicGeometry.Scheme} (f : X.PartialMap Y) (U : X.Opens) (hU : Dense ↑U) (hU' : U ≤ f.domain),
AlgebraicGeometry.IsDominant f.hom ↔ AlgebraicGeometry.IsDominant (f.restrict U hU hU').homf.hom is dominant iff any restriction of f is.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 144 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
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- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
- AlgebraicGeometry.Scheme.Opens.toSchemestatement · cited by 433
- Densestatement and proof · cited by 359
- AlgebraicGeometry.Scheme.PartialMapstatement and proof · cited by 76
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.PartialMap.isDominant_hom_iff_of_equivproof · cited by 2