Theorems · Theorem · algebraic geometry
AlgebraicGeometry.IsOpenImmersion.of_flat_of_mono
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.Flat f]
[AlgebraicGeometry.LocallyOfFinitePresentation f] [CategoryTheory.Mono f], AlgebraicGeometry.IsOpenImmersion fFlat monomorphisms that are locally of finite presentation are open immersions. In particular,
every smooth monomorphism is an open immersion.
The converse holds by inferInstance.
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- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
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