Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.RationalMap.toPartialMap
{X Y : AlgebraicGeometry.Scheme} → [AlgebraicGeometry.IsReduced X] → [Y.IsSeparated] → X.RationalMap Y → X.PartialMap YIf f : X ⤏ Y is a rational map from a reduced scheme to a separated scheme,
then f can be represented as a partial map on its domain of definition.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.CategoryStruct.compproof · cited by 17,999
- CategoryTheory.Iso.invproof · cited by 6,514
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CategoryTheory.PreZeroHypercover.I₀proof · cited by 763
- CategoryTheory.Precoverage.ZeroHypercover.toPreZeroHypercoverproof · cited by 469
- AlgebraicGeometry.Scheme.PartialMapstatement · cited by 76
- AlgebraicGeometry.Scheme.PartialMap.homproof · cited by 49
- AlgebraicGeometry.IsReducedstatement and proof · cited by 38
- AlgebraicGeometry.Scheme.isoOfEqproof · cited by 33
- AlgebraicGeometry.Scheme.RationalMapstatement and proof · cited by 25
- AlgebraicGeometry.Scheme.Cover.glueMorphismsproof · cited by 10
- AlgebraicGeometry.Scheme.IsSeparatedstatement and proof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.PartialMap.toPartialMap_toRationalMap_restrictstatement · cited by 1
- AlgebraicGeometry.Scheme.RationalMap.toPartialMap.congr_simpstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.RationalMap.toRationalMap_toPartialMapstatement and proof · cited by 0