We work out the construction of a Stein manifold from a commutative
Arens-Michael algebra, under assumptions that are mild enough for the process
to be useful in practice. Then, we do the passage to arbitrary complex
manifolds by proposing a suitable notion of scheme. We do this in the abstract
language of spectral functors, in view of its potential usefulness in
non-commutative geometry.Comment: 15 pages. Supported by Fondecyt Postdoctoral Grant No. 311004