2025/11/06 by Siqveland, Arvid
#14A15 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2511.04191
In the article Categorical Construction of Schemes, arXiv:2511.03433 we gave a natural definition of ordinary schemes based on the fact that the localization of a ring in a maximal ideal is a local representation of the corresponding function field. In this text, we replace the category of rings with a general locally small category \cat C, we consider a subcategory \cat B⊂ C of base-points, and assume that each X∈\ob\cat C that contains P∈\ob\cat B, i.e. there is a morphism P→ X, there exists a local representing object XP. Assuming that coproducts exists, we can use the construction of ordinary schemes to construct schemes of objects in any such category.