Theorems · Theorem · algebraic geometry
AlgebraicGeometry.self_of_isIntegral_of_geometrically
∀ {P : CategoryTheory.ObjectProperty AlgebraicGeometry.Scheme} {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y}
[AlgebraicGeometry.IsIntegral Y] [Subsingleton ↥Y], AlgebraicGeometry.geometrically P f → P XThis holds in particular if Y = Spec K.
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- Foundations
- Depth 192 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- AlgebraicGeometry.IsIntegralstatement and proof · cited by 45
- AlgebraicGeometry.geometricallystatement and proof · cited by 26
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