theorem CohomologyPicard.higher_cohomology_vanishes_affine (X : AlgebraicGeometry.Scheme) [AlgebraicGeometry.IsAffine X] (F : X.Modules) [SheafOfModules.IsQuasicoherent F] [CategoryTheory.HasInjectiveResolutions X.Modules] (i : ℕ) (hi : 0 < i) : CategoryTheory.Limits.IsZero (((Scheme.Modules.globalSectionsFunctor X).rightDerived i).obj F)

Higher cohomology of a quasi-coherent sheaf on an affine scheme vanishes (Serre's vanishing theorem for affine schemes).