Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.ord_eq_iff
∀ {X : AlgebraicGeometry.Scheme} [inst : AlgebraicGeometry.IsIntegral X]
[inst_1 : AlgebraicGeometry.IsLocallyNoetherian X] {z : ↥X} (hz : Order.coheight z = 1) {f : ↑X.functionField},
f ≠ 0 →
∀ {n : ℤ},
AlgebraicGeometry.Scheme.ord f z = n ↔ (AlgebraicGeometry.Scheme.ordHom z hz) f = ↑(Multiplicative.ofAdd n)- 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.
Cites25
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Equivstatement · cited by 8,337
- 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
- Multiplicativestatement · cited by 875
Cited by2
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.ord_mulproof · cited by 0
- AlgebraicGeometry.Scheme.ord_of_isUnitproof · cited by 0