Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.ord_le_ord_iff
∀ {X : AlgebraicGeometry.Scheme} [inst : AlgebraicGeometry.IsIntegral X]
[inst_1 : AlgebraicGeometry.IsLocallyNoetherian X] {x y : ↥X} (hx : Order.coheight x = 1) (hy : Order.coheight y = 1)
{f g : ↑X.functionField},
f ≠ 0 →
g ≠ 0 →
(AlgebraicGeometry.Scheme.ord f x ≤ AlgebraicGeometry.Scheme.ord g y ↔
(AlgebraicGeometry.Scheme.ordHom x hx) f ≤ (AlgebraicGeometry.Scheme.ordHom y hy) g)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- 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
- CommRingCat.carrierstatement and proof · cited by 1,096
- Multiplicativestatement · cited by 875
- MonoidWithZeroHomstatement · cited by 704
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.ord_le_smulproof · cited by 0
- AlgebraicGeometry.Scheme.ord_addproof · cited by 0