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For a scheme S I want to consider the spectra of the residue fields of points of S. Is there any way to make this phrase shorter? Is there a term for the morphism that connects such a spectrum with S?

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How about using simply "the point"; in the preliminaries of the paper you could specify that you consider points as schemes by identifying them with spectra of their residue fields. The morphism could be called "the tautological morphism". – Angelo Dec 16 '10 at 10:32
I think it's short enough if you don't have to repeat it all the time. – Martin Brandenburg Dec 16 '10 at 10:37
The residual spectrum ? – Chandan Singh Dalawat Dec 16 '10 at 11:18
Dear Angelo, I thought about "the point"; yet is it natural (and usual) to identify the point with the spectrum of the residue field and not with the corresponding closed subscheme? – Mikhail Bondarko Dec 16 '10 at 16:28
Dear Mikhail, I don't know if it usual, but I do it all the time, and people seem to get it. I certainly would not identify a point with its closure, which is not a very pointlike object. – Angelo Dec 16 '10 at 16:32

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