noncomputable def prop44_affine_pushforward_cohom {X Y : AlgebraicGeometry.Scheme} (f : X ⟶ Y) [AlgebraicGeometry.IsAffineHom f] (F : X.Modules) [SheafOfModules.IsQuasicoherent F] [CategoryTheory.HasInjectiveResolutions X.Modules] [CategoryTheory.HasInjectiveResolutions Y.Modules] (n : ℕ) : ((Scheme.Modules.globalSectionsFunctor Y).rightDerived n).obj ((AlgebraicGeometry.Scheme.Modules.pushforward f).obj F) ≅ ((Scheme.Modules.globalSectionsFunctor X).rightDerived n).obj F

Proposition 44: For an affine morphism f : X → Y and a quasicoherent sheaf F on X, the pushforward preserves higher cohomology: Hⁿ(Y, f_* F) ≅ Hⁿ(X, F).