The dimension of the category of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings of dimension one

Abstract

The dimension of triangulated categories was introduced by Rouquier in 2008 ([5]). As an analogue of this concept, Dao and Takahashi defined the dimension of subcategories of abelian categories in 2014 ([3]). The dimension of categories is an important invariant for studying the structure of both the category and the ground ring when it is the category of modules. For example, the dimension of the category of maximal Cohen-Macaulay modules is zero if the ground ring has finite Cohen-Macaulay representation type. In this paper, we focus on the category of maximal Cohen-Macaulay modules over a hypersurface of dimension one.