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No changes. In “Adams spectral sequences”, It can be proper to justify “AbelianGroups simeq QCoh(Spec(Z))” by linking to affine Serre’s theorem.
I wasn’t aware (anymore) of the old entry affine Serre’s theorem. Somebody should merge whatever of value it contains into Serre-Swan theorem.
As a standalone statement, the affine Serre theorem certainly has value (“whatever of value it contains” suggests there’s something wrong with it; is there?).
I think of the Serre-Swan theorem as more about certain projective modules, which typically lack certain limits and colimits, whereas coherent or quasicoherent modules extend them to repair that loss. So I wouldn’t think to put the latter inside the stomach of the former; instead I’d be more inclined to flesh out the affine Serre theorem article independently (although I’m hardly an expert).
Actually, there may be nits to pick, particularly the title (does anyone call it the “affine Serre theorem”?). It’s not really given a name in Hartshorne, nor in the Stacks Project; there it’s just Lemma or Proposition 13.4 or whatever. Although I have seen the statement mentioned from time to time, as a basic ingredient in calculations, so maybe someone has given it a name after all.
I may jigger around with it a little. It could use some references and maybe some nPOV-ifying.
I think the original reference is the same as Serre’s contribution to Serre-Swan:
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