Gorenstein silting modules and Gorenstein projective modules

TL;DR

This paper introduces Gorenstein silting modules, explores their properties, and establishes connections with Gorenstein projective modules, t-structures, and torsion pairs, providing new insights into their algebraic structure and relationships.

Contribution

It defines Gorenstein silting modules, relates them to 2-term complexes and classical theorems, and characterizes their endomorphism algebras in the context of finite CM-type algebras.

Findings

Partial Gorenstein silting modules are in bijection with τ_G-rigid modules.

Gorenstein silting modules correspond to 2-term Gorenstein silting complexes.

Bounds on global dimension of endomorphism algebras are characterized.

Abstract

(Partial) Gorenstein silting modules are introduced and investigated. It is shown that for finite dimensional algebras of finite CM-type, partial Gorenstein silting modules are in bijection with {\tau}_G-rigid modules; Gorenstein silting modules are the module-theoretic counterpart of 2-term Gorenstein silting complexes; and the relation between 2-term Gorenstein silting complexes, t-structures and torsion pairs in module categories. Furthermore, the corresponding version of the classical Brenner-Butler theorem in this setting are characterised; and the upper bound of the global dimension of endomorphism algebras of 2-term Gorenstein silting complexes over an algebra A are also characterised by terms of the Gorenstein global dimension of A.