# .

# 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 OX, \( H^1(X, I) = 0, \)

then X is affine.

References

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

Retrieved from "http://en.wikipedia.org/"

All text is available under the terms of the GNU Free Documentation License