Theorems · Theorem · algebraic geometry
AlgebraicGeometry.germ_injective_of_isIntegral
∀ (X : AlgebraicGeometry.Scheme) [AlgebraicGeometry.IsIntegral X] {U : X.Opens} (x : ↥X) (hx : x ∈ U),
Function.Injective ⇑(CategoryTheory.ConcreteCategory.hom (X.presheaf.germ U x hx))- Defined in
- Mathlib.AlgebraicGeometry.FunctionField
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 147 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AlgebraicGeometry.IsIntegral
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- Quiver.Homproof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- RingHomstatement · cited by 10,189
- CategoryTheory.Functor.mapproof · cited by 8,698
- 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 and proof · cited by 2,040
- AlgebraicGeometry.PresheafedSpace.carrierstatement and proof · cited by 2,020
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.germToFunctionField_injectiveproof · cited by 0