Categorical representation of locally Noetherian log schemes
The aim of this paper is to show that certain types of schemes can be recovered from categories associated to them. The author starts by studying the case of locally Noetherian schemes. To such a scheme \(X\), he associates the category \(\text{Sch}(X)\) of morphisms of finite type from Noetherian schemes to \(X\). He then shows step by step how to reconstruct \(X\) by purely categorical techniques from the category \(\text{Sch}(X)\). In the second part of the paper, this is extended to fine saturated log schemes whose underlying scheme is locally Noetherian. Here the appropriate category is the category of morphisms from fine saturated log schemes whose underlying scheme is Noetherian and which have the property that the underlying morphism of schemes is of finite type.
scientific article; zbMATH DE number 2105311
scientific article