Theorems · Theorem · algebraic geometry

AlgebraicGeometry.targetAffineLocally_affineAnd_iff

∀ {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
  (RingHom.RespectsIso fun {R S} [CommRing R] [CommRing S] => Q) →
    ∀ {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y),
      AlgebraicGeometry.targetAffineLocally (AlgebraicGeometry.affineAnd fun {R S} [CommRing R] [CommRing S] => Q) f ↔
        ∀ (U : Y.Opens),
          AlgebraicGeometry.IsAffineOpen U →
            AlgebraicGeometry.IsAffineOpen ((TopologicalSpace.Opens.map f.base).obj U) ∧
              Q (CommRingCat.Hom.hom (AlgebraicGeometry.Scheme.Hom.app f U))

Defined in

Mathlib.AlgebraicGeometry.Morphisms.AffineAnd

Cited by

4 results in Mathlib

Foundations

Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound