Theorems · Definition · algebraic geometry
AlgebraicGeometry.Scheme.Hom.residueDegree
{X Y : AlgebraicGeometry.Scheme} → (X ⟶ Y) → ↥X → ℕDegree of f at a point x is defined to be the degree of the associated field extension
from κ(f x) to κ(x). We return a default value of zero when this degree is infinite.
- Defined in
- Mathlib.AlgebraicGeometry.ResidueField
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
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- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpacestatement and proof · cited by 1,892
- Module.finrankproof · cited by 1,770
- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.PresheafedSpace.Hom.baseproof · cited by 1,135
Cited by3
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.residueDegree_idstatement · cited by 1
- AlgebraicGeometry.AlgebraicCycle.mapCoeffproof · cited by 1
- AlgebraicGeometry.AlgebraicCycle.map_idproof · cited by 0