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Localization of Ringed Spaces

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DOI: 10.4236/apm.2011.15045    4,448 Downloads   8,290 Views   Citations

ABSTRACT

Let X be a ringed space together with the data Μ of a set Μ of prime ideals of ΟΧx for each point x∈Χ . We introduce the localization of (X,M') , which is a locally ringed space Y and a map of ringed spaces YΧ enjoying a universal property similar to the localization of a ring at a prime ideal. We use this to prove that the category of locally ringed spaces has all inverse limits, to compare them to the inverse limit in ringed spaces, and to construct a very general Spec functor. We conclude with a discussion of relative schemes.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

W. Gillam, "Localization of Ringed Spaces," Advances in Pure Mathematics, Vol. 1 No. 5, 2011, pp. 250-263. doi: 10.4236/apm.2011.15045.

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