Universality of the category of schemes

Details Universality of the category of schemes Universality of the category of schemes

2012-02-23

arxiv.org/abs/1202.5085v2

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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