Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.ord_eq_zero_of_coheight_neq_one
∀ {X : AlgebraicGeometry.Scheme} [inst : AlgebraicGeometry.IsIntegral X]
[inst_1 : AlgebraicGeometry.IsLocallyNoetherian X] {z : ↥X},
Order.coheight z ≠ 1 → ∀ (f : ↑X.functionField), AlgebraicGeometry.Scheme.ord f z = 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- 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
- Order.coheightstatement and proof · cited by 74
- AlgebraicGeometry.IsIntegralstatement and proof · cited by 45
- AlgebraicGeometry.IsLocallyNoetherianstatement and proof · cited by 31
Cited by5
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.ord_zeroproof · cited by 2
- AlgebraicGeometry.Scheme.ord_le_smulproof · cited by 0
- AlgebraicGeometry.Scheme.ord_mulproof · cited by 0
- AlgebraicGeometry.Scheme.ord_of_isUnitproof · cited by 0
- AlgebraicGeometry.Scheme.ord_addproof · cited by 0