Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsClosedImmersion.isAffine_surjective_of_isAffine
∀ {X Y : AlgebraicGeometry.Scheme} [AlgebraicGeometry.IsAffine Y] (f : X ⟶ Y) [AlgebraicGeometry.IsClosedImmersion f],
AlgebraicGeometry.IsAffine X ∧
Function.Surjective ⇑(CategoryTheory.ConcreteCategory.hom (AlgebraicGeometry.Scheme.Hom.appTop f))If f is a closed immersion with affine target, the source is affine and
the induced map on global sections is surjective.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites44
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.IsClosedImmersion.Spec_iffproof · cited by 1