论文标题
从减少的FS日志方案类别的日志方案的类别理论重建
Category-theoretic Reconstruction of Log Schemes from Categories of Reduced fs Log Schemes
论文作者
论文摘要
令$ s^{\ log} $为本地noetherian fs日志方案，$ \ blacklozenge/s^{\ log} $一组fs log Shemes的属性，上面是$ s^{\ log} $。在本文中，我们将主要关注“简化”的属性，“ Quasi-compact上的$ s^{\ log} $”，“ Quasi-quasi分离超过$ s^{\ log log} $”，“分开$ s^{\ log} $”，而不是$ s^{\ log log log} $ of $ s^{\ log} $。我们将写$ \ Mathsf {sch} _ {\ blacklozenge/s^{\ log}} $，对于$ s^{\ log log} $的完整子类别，由$ s^{\ log log} $确定，由fs log nog noge in cy cangey cangecn $ s^{\ log} $ cancection $ s^{\ log} $ cancection $ s^{\ log。在本文中，我们从抽象类别的内在结构$ \ Mathsf {sch} _ {\ blacklozenge/s^{\ log}} $讨论了日志方案$ s^{\ log} $的纯粹类别理论重建。
Let $S^{\log}$ be a locally Noetherian fs log scheme and $\blacklozenge/S^{\log}$ a set of properties of fs log schemes over $S^{\log}$. In the present paper, we shall mainly be concerned with the properties "reduced", "quasi-compact over $S^{\log}$", "quasi-separated over $S^{\log}$", "separated over $S^{\log}$", and "of finite type over $S^{\log}$". We shall write $\mathsf{Sch}_{\blacklozenge/S^{\log}}$ for the full subcategory of the category of fs log schemes over $S^{\log}$ determined by the fs log schemes over $S^{\log}$ that satisfy every property contained in $\blacklozenge/S^{\log}$. In the present paper, we discuss a purely category-theoretic reconstruction of the log scheme $S^{\log}$ from the intrinsic structure of the abstract category $\mathsf{Sch}_{\blacklozenge/S^{\log}}$.
