A bijection theorem for Gorenstein projective τ-tilting modules.

We introduce the notions of Gorenstein projective τ -rigid modules, Gorenstein projective support τ -tilting modules and Gorenstein torsion pairs and give a Gorenstein analog to Adachi–Iyama–Reiten's bijection theorem on support τ -tilting modules. More precisely, for an algebra Λ , we prove that there is a bijection between the set of Gorenstein projective support τ -tilting modules and the set of functorially finite Gorenstein projective torsion classes. As an application, we introduce the notion of CM- τ -tilting finite algebras and show that Λ is CM- τ -tilting finite if and only if Λ op is CM- τ -tilting finite. Moreover, we show that the Bongartz completion of a Gorenstein projective τ -rigid module need not be a Gorenstein projective τ -tilting module. [ABSTRACT FROM AUTHOR]