Theorems · Theorem · algebraic geometry

AlgebraicGeometry.HasRingHomProperty.descendsAlong_flat

∀ {P : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} [P.IsStableUnderBaseChange]
  {Q : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop}
  [AlgebraicGeometry.HasRingHomProperty P fun {R S} [CommRing R] [CommRing S] => Q],
  (RingHom.CodescendsAlong (fun {R S} [CommRing R] [CommRing S] => Q) fun {R S} [CommRing R] [CommRing S] =>
      RingHom.FaithfullyFlat) →
    P.DescendsAlong (@AlgebraicGeometry.Surjective ⊓ @AlgebraicGeometry.Flat ⊓ @AlgebraicGeometry.QuasiCompact)

Defined in

Mathlib.AlgebraicGeometry.Morphisms.FlatDescent

Cited by

0 results in Mathlib

Foundations

Depth 194 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.MorphismProperty.IsStableUnderBaseChangeAlgebraicGeometry.HasRingHomProperty