Serre's theorem on affineness

In algebraic geometry, given an algebraic variety (or more generally scheme) X, Serre's theorem on affineness, after Jean-Pierre Serre, states that if

(1) X is quasi-compact, and

(2) for every quasi-coherent ideal sheaf I of O_X, $H^1(X, I) = 0$,

then X is affine.

References

• http://stacks.math.columbia.edu/tag/01XF