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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asked Dec 16, 2010 at 10:10
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9$\begingroup$ 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". $\endgroup$– AngeloCommented Dec 16, 2010 at 10:32
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$\begingroup$ I think it's short enough if you don't have to repeat it all the time. $\endgroup$– Martin BrandenburgCommented Dec 16, 2010 at 10:37
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2$\begingroup$ The residual spectrum ? $\endgroup$– Chandan Singh DalawatCommented Dec 16, 2010 at 11:18
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$\begingroup$ 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? $\endgroup$– Mikhail BondarkoCommented Dec 16, 2010 at 16:28
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2$\begingroup$ 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. $\endgroup$– AngeloCommented Dec 16, 2010 at 16:32
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