Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField
{X Y : AlgebraicGeometry.Scheme} →
(f : X ⟶ Y) → (y : ↥Y) → AlgebraicGeometry.Scheme.Hom.fiber f y ⟶ AlgebraicGeometry.Spec (Y.residueField y)The canonical map from the scheme-theoretic fiber to the residue field.
- Defined in
- Mathlib.AlgebraicGeometry.Fiber
- Cited by
- 15 results in Mathlib
- Foundations
- Depth 170 from the axioms · uses propext, Classical.choice, Quot.sound
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 and proof · 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
- CategoryTheory.Limits.pullback.sndproof · cited by 637
- AlgebraicGeometry.Specstatement · cited by 626
- AlgebraicGeometry.Scheme.residueFieldstatement · cited by 95
- AlgebraicGeometry.Scheme.fromSpecResidueFieldproof · cited by 47
Cited by17
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.fiber_facstatement · cited by 2
- AlgebraicGeometry.LocallyQuasiFinite.of_fiberToSpecResidueFieldstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueFieldstatement · cited by 1
- AlgebraicGeometry.isPullback_fiberToSpecResidueField_of_isPullbackstatement and proof · cited by 1
- AlgebraicGeometry.Spec.fiberToSpecResidueFieldIsostatement and proof · cited by 1
- AlgebraicGeometry.Scheme.pointSmallEtaleFiberObjToPreimage_surjectiveproof · cited by 1
- AlgebraicGeometry.Scheme.Hom.fiberOverSpecResidueFieldproof · cited by 0
- AlgebraicGeometry.GeometricallyIrreducible.iff_geometricallyIrreducible_fiberstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField_applystatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Hom.fiber_fac_assocstatement and proof · cited by 0
- AlgebraicGeometry.Scheme.Hom.asFiberHom_fiberToSpecResidueField_assocstatement and proof · cited by 0
- AlgebraicGeometry.locallyQuasiFinite_iff_isFinite_fiberstatement and proof · cited by 0