# Is there an example of a scheme X whose reduction X_red is affine but X is not affine?

For Noetherian schemes this follows from Serre's criterion for affineness by a filtration argument.

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I'm not sure this is a correct answer, but I can't post comments yet -- consider this a comment. How about you take a limit over lots of nilpotent schemes with the same X_red? –  Ilya Nikokoshev Oct 4 '09 at 21:50