Sure he has.. and yes I've seen.. but that doesnt answer the question.. I asked for schemes not prime spectra of commutative rings (otherwise the answer is no.. just take for instance any noncompact space)
@Manny: Yep.. I realized that it should at least be sober and T0 .. but your example with indiscrete two point space is certainly not sober ;) ..
any example/nonexample would be great. Right now Im looking at Hausdorff zero-dimensional spaces (not necessarily Stone), but id like to see the general picture too (so question reduces to weather zero dimensional Hausdorff spaces get map surjectively by the forgetful functor on zero dimensional schemes).. oh wait.. all zero dimensional schemes are T2 arent they?
@David: It's not really a surprise. The profinite groups are Stone spaces, a special form of spectral spaces.. so there must be an affine scheme related to them. So you can do the trick for any profinite group using even Boolean rings.
