Theorems · Theorem · algebraic geometry
AlgebraicGeometry.isOpenImmersion_SpecMap_iff_of_surjective
∀ {R S : CommRingCat} (f : R ⟶ S),
Function.Surjective ⇑(CommRingCat.Hom.hom f) →
(AlgebraicGeometry.IsOpenImmersion (AlgebraicGeometry.Spec.map f) ↔
∃ e, IsIdempotentElem e ∧ RingHom.ker (CommRingCat.Hom.hom f) = Ideal.span {e})Spec (R ⧸ I) ⟶ Spec R is an open immersion iff I is generated by an idempotent.
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- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
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