Silting complexes and Gorenstein projective modules

TL;DR

This paper introduces Gorenstein silting modules and complexes, establishing their relations with classical silting theory, and explores their connections with t-structures, torsion pairs, and endomorphism algebra properties in the context of Gorenstein homological algebra.

Contribution

It defines Gorenstein silting modules and complexes, relates them to existing silting theory, and extends classical results like Brenner-Butler theorem to the Gorenstein setting.

Findings

Gorenstein silting modules are the module-theoretic counterparts of 2-term Gorenstein silting complexes.

Partial Gorenstein silting modules correspond bijectively to τ_G-rigid modules for certain algebras.

The paper characterizes the global dimension of endomorphism algebras of Gorenstein silting complexes.

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.