# .

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 OX, $$H^1(X, I) = 0,$$

then X is affine.
References

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

Mathematics Encyclopedia