Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.Opens.birationalOver_of_dense
∀ {X S : AlgebraicGeometry.Scheme} (U : X.Opens) (sX : X ⟶ S),
Dense ↑U → AlgebraicGeometry.Scheme.BirationalOver (CategoryTheory.CategoryStruct.comp U.ι sX) sXA dense open set U : Opens X of a scheme X over S is S-birational to X.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 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.
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- Top.topproof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- TopCat.carrierstatement · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement · cited by 1,734
- AlgebraicGeometry.Scheme.Opensstatement and proof · cited by 1,149
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Opens.isRationalOver_of_denseproof · cited by 0