论文标题
从减少方案类别的方案的类别理论重建
Category-Theoretic Reconstruction of Schemes from Categories of Reduced Schemes
论文作者
论文摘要
让$ s $是本地的普通计划和$ \ blacklozenge/s $一组$ s $ schemes的属性。然后，我们将为$ s $ s $ -schemes sch $ _ {/s} $的全部子类别编写sch $ _ {\ blacklozenge/s} $，由对象$ x \在{\ rm sch} _ {\ rm sch} _ {\ blacklozenge/s} $中的$ x \ in {\ rm sch} in {\ rm sch} in {\ rm sch} $确定。在本文中，我们将主要关注“降低”的属性，“超过$ s $”，“ Quasi-compact”，“超过$ S $”和“超过$ S $”的属性。我们给出了一种功能性类别理论算法，用于从抽象类别的内在结构sch $ _ {\ blacklozenge/s} $重建$ s $。该结果类似于Mochizuki \ cite {mzk04}的结果，并且在$ s $是本地的正常方案的情况下，可能被视为de bruyn \ cite {debr19}结果的部分概括。
Let $S$ be a locally Noetherian normal scheme and $\blacklozenge/S$ a set of properties of $S$-schemes. Then we shall write Sch$_{\blacklozenge/S}$ for the full subcategory of the category of $S$-schemes Sch$_{/S}$ determined by the objects $X\in {\rm Sch}_{\blacklozenge/S}$ that satisfy every property of $\blacklozenge/S$. In the present paper, we shall mainly be concerned with the properties "reduced", "quasi-compact over $S$", "quasi-separated over $S$", and "separated over $S$". We give a functorial category-theoretic algorithm for reconstructing $S$ from the intrinsic structure of the abstract category Sch$_{\blacklozenge/S}$. This result is analogous to a result of Mochizuki \cite{Mzk04} and may be regarded as a partial generalization of a result of de Bruyn \cite{deBr19} in the case where $S$ is a locally Noetherian normal scheme.
