Silting complexes and Gorenstein projective modules (2110.12161v2)

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.