Serre's theorem on affineness

Statement

Related results

• A special case of this theorem arises when is an algebraic variety, in which case the conditions of the theorem imply that is an affine variety.
• A similar result has stricter conditions on but looser conditions on the cohomology: if is a quasi-separated, quasi-compact scheme, and if for any quasi-coherent sheaf of ideals of finite type, then is affine.