Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isFinite_iff_locallyOfFiniteType_of_jacobsonSpace
∀ {X Y : AlgebraicGeometry.Scheme} {f : X ⟶ Y} [Subsingleton ↥X] [AlgebraicGeometry.IsReduced X] [JacobsonSpace ↥Y],
AlgebraicGeometry.IsFinite f ↔ AlgebraicGeometry.LocallyOfFiniteType fIf X is a Jacobson scheme and k is a field,
Spec(k) ⟶ X is finite iff it is (locally) of finite type.
(The statement is more general to allow the empty scheme as well)
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 223 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites60
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.closePoints_subset_preimage_closedPointsproof · cited by 1