Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isIso_of_isClosedImmersion_of_surjective
∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.IsClosedImmersion f] [AlgebraicGeometry.Surjective f]
[AlgebraicGeometry.IsReduced Y], CategoryTheory.IsIso fA surjective closed immersion is an isomorphism when the target is reduced.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 220 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- AlgebraicGeometry.Schemestatement and proof · cited by 2,540
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- AlgebraicGeometry.LocallyRingedSpace.toSheafedSpaceproof · cited by 1,892
- AlgebraicGeometry.Scheme.toLocallyRingedSpaceproof · cited by 1,734
- closureproof · cited by 1,254
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.ext_of_isDominant_of_isSeparatedproof · cited by 3