Silting complexes and Gorenstein projective modules
Abstract
We introduce Gorenstein silting modules (resp. complexes), and give the relation with the usual silting modules (resp. complexes). We show that Gorenstein silting modules are the module-theoretic counterpart of 2-term Gorenstein silting complexes; and partial Gorenstein silting modules are in bijection with \tau_{G}-rigid modules for finite dimensional algebras of finite CM-type. We also give the relation between 2-term Gorenstein silting complexes, t-structures and torsion pair in module categories; and generalise the classical Brenner-Butler theorem to this setting; and characterise the global dimension of endomorphism algebras of 2-term Gorenstein silting complexes over an algebra A by terms of the Gorenstein global dimension of A.
Cite
@article{arxiv.2110.12161,
title = {Silting complexes and Gorenstein projective modules},
author = {Nan Gao and Jing Ma and Chiheng Zhang},
journal= {arXiv preprint arXiv:2110.12161},
year = {2021}
}
Comments
21 pages; On the basis of the previous version of the paper, we have added the content of further research