论文标题
按照指示的flat flat准连轴滑带和准固体结转周期性
Flat quasi-coherent sheaves as directed colimits, and quasi-coherent cotorsion periodicity
论文作者
论文摘要
我们表明，在准紧凑的准分离方案上，每种平面的准固定捆起来都是局部可计数的扁平式准搭换滑轮的定向性。更一般而言，对于任何可计数的准压缩，可计数分离的方案，相同的断言都存在。此外，对于三类扁平准固定滑轮的复合物，我们表明该类别中的所有复合物都可以作为来自同一类别的局部可计数式扁平准固定带的局部可计数的综合体获得。特别是，在准混合半分离的方案上，每个平面准固定的捆框都是有限的投影尺寸的扁平准固定滑轮的定向性。在本文的第二部分中，我们讨论了类别理论环境中的Cotorsion周期性，从而推广了Bazzoni，Cortes-izurdiaga和Estrada的论点。作为主要应用程序，我们推断出任何在准紧凑型半分隔方案上的任何cotorsion-周期性准固定式的捆绑都是cotorsion。
We show that every flat quasi-coherent sheaf on a quasi-compact quasi-separated scheme is a directed colimit of locally countably presentable flat quasi-coherent sheaves. More generally, the same assertion holds for any countably quasi-compact, countably quasi-separated scheme. Moreover, for three categories of complexes of flat quasi-coherent sheaves, we show that all complexes in the category can be obtained as directed colimits of complexes of locally countably presentable flat quasi-coherent sheaves from the same category. In particular, on a quasi-compact semi-separated scheme, every flat quasi-coherent sheaf is a directed colimit of flat quasi-coherent sheaves of finite projective dimension. In the second part of the paper, we discuss cotorsion periodicity in category-theoretic context, generalizing an argument of Bazzoni, Cortes-Izurdiaga, and Estrada. As the main application, we deduce the assertion that any cotorsion-periodic quasi-coherent sheaf on a quasi-compact semi-separated scheme is cotorsion.
