Stable categories of spherical modules and torsionfree modules

Author:

Otake Yuya

Abstract

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 n -spherical modules and n n -torsionfree modules. In this paper, we construct an equivalence between the stable category of n n -spherical modules and the category of modules of grade at least n n , and provide its Gorenstein analogue. As an application, we prove that if R R is a Gorenstein local ring of Krull dimension d > 0 d>0 , then there exists a stable equivalence between the category of ( d 1 ) (d-1) -torsionfree R R -modules and the category of d d -spherical modules relative to the local cohomology functor.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference9 articles.

1. Memoirs of the American Mathematical Society, No. 94;Auslander, Maurice,1969

2. Cambridge Studies in Advanced Mathematics;Brodmann, M. P.,1998

3. Cambridge Studies in Advanced Mathematics;Bruns, Winfried,1993

4. On the subcategories of 𝑛-torsionfree modules and related modules;Dey, Souvik;Collect. Math.,2023

5. London Mathematical Society Lecture Note Series;Evans, E. Graham,1985

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