论文标题
卡地亚晶体具有有限的全球维度
Cartier Crystals have finite global dimension
论文作者
论文摘要
我们表明，准连续性卡地亚晶体的类别相当于Finite Noetherian环R上的单元卡地亚模块类别，并且这些等效类别具有有限的全局维度，表明每个准核糖卡地台晶体都有有限的注入分辨率分辨率。分辨率的长度仅取决于R的限制。我们的结果应视为MA结果的概括，表明F-FiNite常规环R上的单位R [F]模块的类别具有有限的全局尺寸dim r + 1。
We show that the category of quasi-coherent Cartier crystals is equivalent to the category of unit Cartier modules on an F-finite noetherian ring R, and that these equivalent categories have finite global dimension, by showing that every quasi-coherent Cartier crystal has a finite injective resolution. The length of the resolution is uniformly bounded by a bound only depending on R. Our result should be viewed as a generalization of a result of Ma showing that the category of unit R[F]-modules over a F-finite regular ring R has finite global dimension dim R + 1.
