论文标题
确切的类别，大型科恩 - 马库拉模块和有限表示类型
Exact categories, big Cohen-Macaulay modules and finite representation type
论文作者
论文摘要
由于Auslander和Ringel-Tachikawa，Artin代数代表理论的第一个显着结果之一是Artin代数为代表限制时的表征。在本文中，我们在Quillen的意义上研究了确切类别的一般背景中表示代表性的方面。在此框架中，我们介绍“大对象”，并证明了Auslander型“拆分型”定理。我们的方法通用并统一了文献的已知结果。作为我们方法的进一步应用，我们将Auslander和Ringel-Tachikawa的定理扩展到任意维度，即，在完整的常规局部环上的Cohen-Macaulay订单表征何时是有限表示的。
One of the first remarkable results in the representation theory of artin algebras, due to Auslander and Ringel-Tachikawa, is the characterization of when an artin algebra is representation-finite. In this paper, we investigate aspects of representation-finiteness in the general context of exact categories in the sense of Quillen. In this framework, we introduce "big objects" and prove an Auslander-type "splitting-big-objects" theorem. Our approach generalises and unifies the known results from the literature. As a further application of our methods, we extend the theorems of Auslander and Ringel-Tachikawa to arbitrary dimension, i.e. we characterise when a Cohen-Macaulay order over a complete regular local ring is of finite representation type.
