Theorems · Theorem · algebraic geometry
AlgebraicGeometry.Scheme.ord_of_isUnit
∀ {X : AlgebraicGeometry.Scheme} [inst : AlgebraicGeometry.IsIntegral X]
[inst_1 : AlgebraicGeometry.IsLocallyNoetherian X] {U : X.Opens} [inst_2 : Nonempty ↥↑U]
{f : ↑(X.presheaf.obj (Opposite.op U))},
IsUnit f →
∀ {x : ↥X},
x ∈ U → AlgebraicGeometry.Scheme.ord ((CategoryTheory.ConcreteCategory.hom (X.germToFunctionField U)) f) x = 0- Cited by
- 0 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites28
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
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- RingHomstatement · cited by 10,189
- Oppositestatement · cited by 8,081
- CategoryTheory.ConcreteCategory.homstatement and proof · cited by 4,022
- TopCat.carrierstatement and proof · cited by 3,184
- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
- CommRingCatstatement · cited by 2,333
- TopologicalSpace.Opensstatement · cited by 2,040
- 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
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