Theorems · Inductive type · algebraic geometry
AlgebraicGeometry.IsIntegral
AlgebraicGeometry.Scheme → Prop
A scheme X is integral if its is nonempty,
and 𝒪ₓ(U) is an integral domain for each U ≠ ∅.
- Defined in
- Mathlib.AlgebraicGeometry.Properties
- Cited by
- 45 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AlgebraicGeometry.Schemestatement · cited by 2,540
Cited by54
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.ordstatement and proof · cited by 12
- AlgebraicGeometry.Scheme.ordHomstatement and proof · cited by 10
- AlgebraicGeometry.Scheme.ord_eq_zero_of_coheight_neq_onestatement and proof · cited by 5
- AlgebraicGeometry.isIntegral_of_irreducibleSpace_of_isReducedstatement · cited by 3
- AlgebraicGeometry.Scheme.ord_eq_unzero_ordHomstatement and proof · cited by 3
- AlgebraicGeometry.isIntegral_iff_irreducibleSpace_and_isReducedstatement and proof · cited by 2
- AlgebraicGeometry.isIntegral_of_isOpenImmersionstatement and proof · cited by 2
- AlgebraicGeometry.geometrically_eq_universallystatement and proof · cited by 2
- AlgebraicGeometry.Scheme.ord.congr_simpstatement and proof · cited by 2
- AlgebraicGeometry.GeometricallyIntegral.eq_geometricallystatement · cited by 2
- AlgebraicGeometry.Scheme.ord_eq_iffstatement and proof · cited by 2
- AlgebraicGeometry.Scheme.ord_eq_ordHom_of_coheight_eq_onestatement and proof · cited by 2