Universality of the category of schemes

Satoshi Takagi

Published 2012-02-23, updated 2012-06-10Version 3

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.