Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Hom.birationalOver
∀ {X U S : AlgebraicGeometry.Scheme} (f : U ⟶ X) [AlgebraicGeometry.IsOpenImmersion f] [AlgebraicGeometry.IsDominant f]
(sX : X ⟶ S) (sU : U ⟶ S),
CategoryTheory.CategoryStruct.comp f sX = sU → AlgebraicGeometry.Scheme.BirationalOver sU sX- Cited by
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- Foundations
- Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites23
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
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- Top.topproof · cited by 9,680
- CategoryTheory.Iso.homproof · cited by 7,684
- CategoryTheory.Category.assocproof · cited by 6,433
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.Iso.symmproof · cited by 993
- CategoryTheory.Iso.transproof · cited by 566
- AlgebraicGeometry.IsOpenImmersionstatement and proof · cited by 476
- AlgebraicGeometry.Scheme.Opens.toSchemeproof · cited by 433
- AlgebraicGeometry.Scheme.Opens.ιproof · cited by 275
- AlgebraicGeometry.Scheme.Hom.opensRangeproof · cited by 113
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