Mathematics – Algebraic Geometry
Scientific paper
2012-02-23
Mathematics
Algebraic Geometry
35 pages, revised Feb. 24, 2012
Scientific paper
In this paper, we generalize the construction method of schemes to other algebraic categories, and show that the category of coherent schemes can be characterized by a universal property, if we fix the class of Grothendieck topology. Also, we introduce the notion of $\scr{C}$-schemes, which is a further generalization of coherent schemes and still shares common properties with ordinary schemes.
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