Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.RationalMap.fromFunctionField
{X Y : AlgebraicGeometry.Scheme} →
[inst : IrreducibleSpace ↥X] → X.RationalMap Y → (AlgebraicGeometry.Spec X.functionField ⟶ Y)A rational map restricts to a map from Spec K(X).
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- IrreducibleSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Quiver.Homstatement · cited by 32,603
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
- AlgebraicGeometry.SheafedSpace.toPresheafedSpacestatement and proof · cited by 1,988
- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.Specstatement · cited by 626
- IrreducibleSpacestatement and proof · cited by 40
- AlgebraicGeometry.Scheme.RationalMapstatement and proof · cited by 25
- AlgebraicGeometry.Scheme.functionFieldstatement · cited by 23
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.RationalMap.eq_of_fromFunctionField_eqstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.RationalMap.equivFunctionFieldproof · cited by 0
- AlgebraicGeometry.Scheme.RationalMap.fromFunctionField_ofFunctionFieldstatement · cited by 0
- AlgebraicGeometry.Scheme.RationalMap.fromFunctionField_toRationalMapstatement · cited by 0