STABLE CATEGORIES OF SPHERICAL MODULES AND TORSIONFREE MODULES

Auslander and Bridger [Stable module theory, Memoirs of the American Mathematical Society, No. 94, American Mathematical Society, Providence, R.I., 1969] introduced the notions of n -spherical modules and ntorsionfree modules. In this paper, we construct an equivalence between the stable category of n -spherical modules and the category of modules of grade at least n, and provide its Gorenstein analogue. As an application, we prove that if R is a Gorenstein local ring of Krull dimension d > 0, then there exists a stable equivalence between the category of (d-1)-torsionfree R -modules and the category of d -spherical modules relative to the local cohomology functor.