# 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}, ,

then *X* is affine.

## References

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