Theorems · Theorem · algebraic geometry
AlgebraicGeometry.geometrically_iff_forall_fiberToSpecResidueField
∀ {P : CategoryTheory.ObjectProperty AlgebraicGeometry.Scheme} {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y},
AlgebraicGeometry.geometrically P f ↔
∀ (y : ↥Y), AlgebraicGeometry.geometrically P (AlgebraicGeometry.Scheme.Hom.fiberToSpecResidueField f y)P holds geometrically for f if and only if all fibers are geometrically P.
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- Foundations
- Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
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