A bijection theorem for Gorenstein projective t-tilting modules

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