Theorems · Theorem · algebraic geometry
AlgebraicGeometry.GeometricallyIntegral.iff_geometricallyIntegral_fiber
∀ {X S : AlgebraicGeometry.Scheme} (f : X ⟶ S),
AlgebraicGeometry.GeometricallyIntegral f ↔
∀ (s : ↥S), AlgebraicGeometry.GeometricallyIntegral (AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField f s)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 195 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- AlgebraicGeometry.Scheme.toLocallyRingedSpacestatement and proof · cited by 1,734
- AlgebraicGeometry.Specstatement and proof · cited by 626
- AlgebraicGeometry.Scheme.residueFieldstatement and proof · cited by 95
- AlgebraicGeometry.IsIntegralproof · cited by 45
- AlgebraicGeometry.Scheme.Hom.fiberstatement and proof · cited by 30
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