부산대학교 도서관

A new notion of depth of an object X with respect to a homogeneous ideal a , depth R (a , X) , is introduced for a compactly generated triangulated category T ; the local nature and some basic properties of depth R (a , X) are provided. What's more, we give a computation of the dimension dim R X of objects in T , and prove that if (R , m) is a graded local ring, then depth R (a , X) ⩽ dim R X + inf X for every cohomologically finite object X in T . [ABSTRACT FROM AUTHOR]