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arXiv · 2110.12161

Silting complexes and Gorenstein projective modules

Nan Gao·Jing Ma·Chiheng Zhang
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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.

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Nan Gao, Jing Ma, Chiheng Zhang. 2021-10-23. Silting complexes and Gorenstein projective modules. https://arxiv.org/abs/2110.12161

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